METODY ILOŚCIOWE W BADANIACH EKONOMICZNYCH


 Magdalene Gilmore
 2 years ago
 Views:
Transcription
1 Warsaw Unversty of Lfe Scences SGGW Faculty of Appled Informatcs and Mathematcs METODY ILOŚCIOWE W BADANIACH EKONOMICZNYCH QUANTITATIVE METHODS IN ECONOMICS Volume XII, No. EDITORINCHIEF Bolesław Borkowsk Warsaw 20
2 EDITORIAL BOARD Prof. Zbgnew Bnderman char, Prof. Bolesław Borkowsk, Prof. Leszek Kuchar, Prof. Wojcech Zelńsk, Dr. hab. Stansław Gędek, Dr. Hanna Dudek, Dr. Agata Bnderman Secretary SCIENTIFIC BOARD Prof. Bolesław Borkowsk char (Warsaw Unversty of Lfe Scences SGGW), Prof. Zbgnew Bnderman (Warsaw Unversty of Lfe Scences SGGW), Prof. Paolo Gajo (Unversty of Florence, Italy), Prof. Evgeny Grebenkov (Computng Centre of Russa Academy of Scences, Moscow, Russa), Prof. Yury Kondratenko (Black Sea State Unversty, Ukrane), Prof. Vassls Kostoglou (Alexander Technologcal Educatonal Insttute of Thessalonk, Greece), Prof. Robert Kragler (Unversty of Appled Scences, Wengarten, Germany), Prof. Yochanan Shachmurove (The Cty College of The Cty Unversty of New York), Prof. Alexander N. Prokopenya (Brest Unversty, Belarus), Dr. Monka Krawec Secretary (Warsaw Unversty of Lfe Scences SGGW). PREPARATION OF THE CAMERA READY COPY Dr. Jolanta Kotlarska, Dr. Elżbeta Saganowska TECHNICAL EDITORS Dr. Jolanta Kotlarska, Dr. Elżbeta Saganowska LIST OF REVIEWERS Prof. Iacopo Bernett (Unversty of Florence, Italy) Prof. Paolo Gajo (Unversty of Florence, Italy) Prof. Yury Kondratenko (Black Sea State Unversty, Ukrane) Prof. Vassls Kostoglou (Alexander Technologcal Educatonal Insttute of Thessalonk, Greece), Prof. Karol Kukuła (Unversty of Agrculture n Krakow) Prof. Wanda MarcnkowskaLewandowska (Warsaw School of Economcs) Prof. Yochanan Shachmurove (The Cty College of the Cty Unversty of New York) Prof. Ewa Marta Syczewska (Warsaw School of Economcs) Prof. Dorota Wtkowska (Warsaw Unversty of Lfe Scences SGGW) Prof. Wojcech Zelńsk (Warsaw Unversty of Lfe Scences SGGW) Dr. Lucyna BłażejczykMajka (Adam Mckewcz Unversty n Poznan) Dr. Mchaela Chocolata (Unversty of Economcs n Bratslava, Slovaka) ISSN X Copyrght by Katedra Ekonometr Statystyk SGGW Warsaw 20, Volume XII, No. Publshed by Warsaw Unversty of Lfe Scences Press
3 CONTENTS Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny An applcaton of radar charts to geometrcal measures of structures of conformablty... Zbgnew Bnderman, Marek Werzbck Some remarks on aplcatons of algebrac analyss to economcs... 5 Mchaela Chocholatá Tradng volume and volatlty of stock returns: Evdence from some European and Asan stock markets Marcn Dudzńsk, Konrad Furmańczyk The quantle estmaton of the maxma of sea levels E. M. Ekanayake, Lucyna Korneck Factors affectng nward foregn drect nvestment flows nto the Unted States: Evdence from StateLevel Data Andrea Furková, Kvetoslava Surmanová Stochastc fronter analyss of regonal compettveness Jarosław Jankowsk Identfcaton of web platforms usage patterns wth dynamc tme seres analyss methods Stansław Jaworsk, Konrad Furmańczyk On the choce of parameters of changepont detecton wth applcaton to stock exchange data Krzysztof Karpo, Arkadusz Orłowsk, Potr Łukasewcz, Jerzy Różańsk Some applcatons of rank clocks method Monka Krawec Effcency of ndrect ways of nvestng n commodtes n condtons of polsh captal market Mara Parlńska, Galsan Dareev Applcatons of producton functon n agrculture... 9 Grzegorz Przekota, Tadeusz Waścńsk, Lda Sobczak Reacton of the nterest rates n Poland to the nterest rates changes n the USA and euro zone... 25
4 4 Contents Aleksander Strasburger, Andrzej Zembrzusk On applcaton of Newton s Method to solve optmzaton problems n the consumer theory. Expanson s Paths and Engel Curves Ewa Marta Syczewska Contegraton snce Granger: evoluton and development Tadeusz Waścńsk, Grzegorz Przekota, Lda Sobczak Behavor of the Central Europe exchange rates to the Euro and US dollar Wojcech Zelńsk Comparson of confdence ntervals for fracton n fnte populatons... 77
5 QUANTITATIVE METHODS IN ECONOMICS Vol. XII, No., 20, pp. 3 AN APPLICATION OF RADAR CHARTS TO GEOMETRICAL MEASURES OF STRUCTURES OF CONFORMABILITY Zbgnew Bnderman, Bolesław Borkowsk Department of Econometrcs and Statstcs, Warsaw Unversty of Lve Scences SGGW emals: Wesław Szczesny Department of Informatcs, Warsaw Unversty of Lve Scences SGGW emal: Abstract: In the followng work we presented a method of usng radar charts to calculate measures of conformablty of two objects accordng to formulas gven by, among others, Dce, Jaccard, Tanmoto and Tversky. Ths method ncorporates another one presented by the authors of ths study [Bnderman, Borkowsk, Szczesny 200]. Presented methods can be also utlzed to defne smlartes between gven objects, as well as to order and group objects. Measures descrbed n ths work satsfy the condton of stablty as they do not depend on the order of studed features. Key words: radar method, radar measure of conformablty, Dce s, Jaccard s measure of smlarty, synthetc measures, classfcaton, cluster analyss. CONSTRUCTION OF RADAR MEASURES OF CONFORMABILITY In prevous works authors used methods that have a smple nterpretaton n the form of a radar chart to order, classfy and measure smlarty of objects [Bnderman, Borkowsk, Szczesny 2008, 2009, 2009a, 200, 200a, b, c, d, Bnderman, Szczesny 2009, 20, Bnderman 2009, 2009a]. Those methods do not depend on the way the features of a gven object are ordered. In the followng work authors attempted to utlze those methods n other, wdely known means of measurng smlarty between two objects. Comparng structures of objects s chosen here as an example. Coeffcents of Jaccard, Dce and Tanmoto, Tversky ndex and cosne smlarty are all exemplary geometrcal measures of smlarty.
6 2 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny The methods presented here may seem numercally complcated but n the age of computers ths problem s of lttle sgnfcance. Numerous studes conducted n many dfferent felds of scence: economcs, statstcs, computer scence, chemstry, bology, ecology, psychology, culture and toursm have proven the usefulness of those methods [Bnderman 2009a, Bnderman, Borkowsk, Szczesny 200b, c, Cok, Kowalczyk, Pleszczyńska, Szczesny 995, Deza E., Deza M.M. 2006, Duda, Hart, Stork 2000, Gordon 999, Hubalek 982, Kukuła 2000, 200, Legendre P., Legendre L. 998, Monev 2004, Szczesny 2002, Tan, Stenbach, Kumar 2006, Warrens 2008]. Let Q and P be two objects that are descrbed by a set of n (n>2) features. n Assume that objects Q and P are descrbed by two vectors x, y R +, where: x = ( x, x2,..., xn), y = ( y, y2,..., yn); x, y 0; = 2,,..., n and n n x =, y =. = = In order to graphcally represent the methods we nscrbe a regular ngon nto a unt crcle (wth a radus of ) wth a centre n the orgn of a polar coordnate system 0uv and we wll connect the vertces of ths ngon wth the orgn of the coordnate system. Thus, one constructs lne segments of length, we wll denote, n sequence, O,O2,...,0n, startng, for defntveness, wth the lne segment coverng w axs. Assume that at least two coordnates of each of the vectors x and y are nonzero. Because features of objects x and y take on values from an nterval <0,>, that s 0 x 0 x, 0 y 0 y, =,2,...n, where 0:=(0,0,...,0), :=(,,...,), we can represent the values of those features as a radar chart. To do so, let x (y ) denote those ponts on the 0 axs that came nto beng by ntersectng the 0 axs wth a crcle wth the centre at the orgn of the coordnate system and radus of x (y ), =,2,...,n. By connectng the ponts: x wth x 2, x 2 wth x 3,..., x n wth x (y wth y 2, y 2 wth y 3,..., y n wth y ) we get ngons S Q and S P, where ts areas S Q and S P, are gven by formulas: n n 2π 2π SQ = Sx = : n 2xx sn = sn, gdze, + n 2 n xx x = + + x = = () n n 2π 2π SP = Sy = sn sn, gdze :. 2yy = n 2 yy y = y + n + n+ = = The formula for the area of the ntersecton of those ngons, whch we wll denote by Sx y : = Sx Sy has a more complcated form. Its form and detaled determnaton can be found n [Bnderman, Borkowsk, Szczesny 200]. Usng those formulae we can denote the area of the unon of ngons S x and S y as
7 An applcaton of radar charts 3 Sx Sy = Sx + Sy Sx S y, (2) where the areas Sx, Sy are defned by formulae (). Fgure presents two graphcal llustratons of vectors x=(0,2, 0,2, 0,3, 0,5, 0,, 0,05) and y =(0,5, 0,5, 0,2, 0,25, 0,5, 0,) that descrbe two exemplary demographcal structures (for age ranges: 04, 524, 2549, 5064, 6579, >80), whle Fg. A and B dffer only by the order of axes (meanng the permutaton of the coordnates). Fg.. Radar charts for vectors x and y, whch coordnates present two exemplary demographcal structures, by dfferent orderng of axes. > ,3 0,25 0,2 0,5 0, 0, > B 04 0,3 0,25 0,2 0,5 0, 0, A Source: own work From the fgure t s clear that areas of ngons Sx, S y and ther unons on fgures A and B dffer n sze. They are: 0,076; 0,074; 0,05 and 0,075; 0,069; 0,047, respectvely. In works [Bnderman Borkowsk, Szczesny 2008, 200] authors proposed a measure of conformablty of objects that uses a geometrcal nterpretaton n the form of radar charts and s defned as follows: R xy = S S x y σ xy S S x y ω xy for n= 3 for n 4, () 3
8 4 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny where mn( S gdy > 0 gdy > 0 x, S y ) S x S y max( S x, S y ) S x S y xy gdy Sx Sy= 0 gdy Sx Sy= 0 σ : =, ω : = xy. Note that such a measure of conformablty (smlarty) has the property of: 0 μ x.y and depends on the orderng of features [cf. Bnderman Borkowsk, Szczesny 2008]. To defne a measure of conformablty of objects that does not depend on the orderng of features, let us denote by π j a jth permutaton of numbers,2,,n. It s known that the number of all such permutatons s equal to n! [Mostowsk, Stark 977]. Each permutaton of coordnates of vectors x and y corresponds to one permutaton π j. Let vectors x j, y j denote the jth permutaton of coordnates of vectors x and y, respectvely, assumng that x :=x, y :=y. For example, f n=3, x=(x,x 2,x 3 ), y=(y,y 2,y 3 ) and π =(,2,3), π 2 =(,3,2), π 3 =(2,,3), π 4 =(2,3,), π 5 =(3,,2), π 6 =(3,2,) then: x =(x,x 2,x 3 ), y =(y,y 2,y 3 ), x 2 =(x,x 3,x 2 ), y 2 =(y,y 3,y 2 ) x 3 =(x 2,x,x 3 ), y 3 =(y 2,y,y 3 ), x 4 =(x 2,x 3,x ), y 4 =(y 2,y 3,y ), x 5 =(x 3,x,x 2 ), y 5 =(y 3,y,y 2 ), x 6 =(x 3,x 2,x ), y 6 =(y 3,y 2,y ). A result from our earler works s that a coeffcent of conformablty of structures corresponds to each jth permutaton x j, y j of coordnates of vectors x and y j RQP, = R xy, ( 4) j j where naturally RQP, = R xy. Therefore, we can assume that the followng desgnatons of three dfferent measures of conformablty of consdered objects Q and P. Naturally, those measures are nvarant under the orderng of coordnates for vectors x and y. M M j QP, = xy = QP, j n! m m j QP, = xy = QP, j n! n! s s j QP, = xy = QP,. n! j= R R max R, R R mn R, () 5 R R R
9 An applcaton of radar charts 5 Other wellknown n lterature technques that use geometrcal nterpretatons, such as radar charts, may be used to compare two structures x = ( x, x2,..., xn), y = ( y, y2,..., y n). Most well known among them are: cosne smlarty [Deza, Deza 2006] Sx Sy for S S > 0 c x y S S, xy x y (6) = 0 for Sx Sy = 0 Jaccard coeffcent [Jaccard 90, 902, 908] Sx Sy for S S 0 J x y > xy = Sx Sy, 0 for Sx Sy = 0 (7) Dce s coeffcent [Dce 945] 2Sx Sy for Sx Sy > 0 D xy = Sx + Sy, (8) 0 for Sx Sy = 0 Tanmoto coeffcent [Tanmoto 957, 959] Sx Sy for Sx Sy > 0 T xy = Sx + Sy Sx S y, (9) 0 for Sx Sy = 0
10 6 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny Tversky ndex [Tversky 957] S S x y for Sx Sy > 0 xy Sx Sy + α S x \Sy + β S y \Sx, T = αβ 0. (0) 0 for Sx Sy = 0 Let us note that f n the above formula the coeffcents fulfll α=β= then we get Tanmoto s formula and f α=β= then we get Dce s formula. Here and n 2 the sequel we shall assume that α=β=. 4 Note that the defned above measures of smlarty, take a value between [0, ], are dependent on the orderng of features n case once represents the object by a radar chart. Another smple way of vsualzng the structure x = ( x, x2,..., xn ) s a bar graph, n whch each coordnate s represented as a rectangle of wdth and heght x (for =,,n). The area of such graph s equal to and one of the most popular ndcators of smlarty of two structures x = ( x, x2,..., xn ) and y = ( y, y2,..., y n ) s defned as [Malna 2004]: n Wxy : = mn( x, y), () = It s clear that ts value s ndependent of the orderng of features and, n the case of such graphcal representaton of structure, takes a value dentcal to the values of coeffcents defned n (6) and (8). In every stuaton when the ndcator of smlarty of two structures that uses a graphcal nterpretaton s not nvarant under the permutaton of coordnates, we may modfy ts defnton, n a way shown above (see formula (5)). Thus, to defne a measure of conformablty that would be ndependent of the orderng of features, let us denote by p j the jth permutaton of numbers,2,,n. Naturally, each permutaton of coordnates of vectors x and y corresponds to one permutaton p j. Let vectors x j, y j denote jth permutaton of coordnates of vectors x and y, respectvely. Assume that x =x, y =y, for each jth permutaton x j, y j of coordnates of vectors x and y corresponds a coeffcent of conformablty of structures j c, = cxy, ( 2) j j QP
11 An applcaton of radar charts 7 where naturally c QP, = c xy, and the cosne smlarty c xy s defned as n formula (6). Wth regard to the above, let us assume the followng defntons of three dfferent measures of conformablty for objects Q and P M M j QP, = x,y = QP, j n! m m j QP, = x,y = QP, j n! n! s s j QP, = x,y = QP, n! j= c c max c, c c mn c, ( 3) c c c. In a smlar manner we can defne other coeffcents M m s M m s M m s M m s J xy,j xy,j xy;d xy,d xy, D xy ; Txy, Txy, T xy;t xy,txytxy. In order to demonstrate the presented above method of comparng structures, let us consder a smple example. Example. Let Q= x=,, 0, R= y =,,. Let us assume the followng denotatons: x: = x4 : = x, x2 : = x5: =,0,, x3: = x6 : = 0,,, y: = y2 : = y3: = y4 : = y5: = y6 = y. Thus we have: 2π 3 2π 3 Sx = sn =, S 3 sn, y = = π Sx S sn,, y = = S x S y = Rxy = / =, dla =,2,...,
12 8 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny M m s 2 So Rx,y = Rx,y = Rx,y = = ~, M s m, where coeffcents RQP,, RQP,, R QP, are defned as n formulae (5). It can be easly verfed that coeffcents of conformablty of structures: cosne (formula (3)), Jaccard, Dce s are equal to: M m s M m s M m s c = c = c = 0, 385; J = J = J = 0, 236; D = D = D = 0, 38. x,y x,y x,y x,y x,y x,y x,y x,y x,y Note that M M M c = 0620, ; J = 0486, ; D = 067,. x,y x,y x,y It s also noteworthy that n ths case the coeffcent of conformablty of structures 2 (defned by formula ()) s W xy = =. The value of the coeffcent defne by formula (7) or (9) that uses an nterpretaton of the structure as a bar graph s equal to 0,5 =0,6(6)/,3(3). The above example shows that measures of smlarty of two objects calculated by dfferent methods (e.g. a method that ncludes the manner of the graphcal representaton of the structure or a method of normalzng, whch, when appled, causes the measure of the area of the unon of faces to take a value between [0, ]), can be sgnfcantly dfferent. A sngle measure of smlarty of objects can be far from optmal n the understandng of a gven expert. Furthermore, experts can dsagree on the meanngs of ndvdual measures. Thus t s safer to use, n the analyss of structures, a measure that s, for example, an average of several dfferent measures of smlarty [see: Breman 994]. EMPIRICAL RESULTS In order to verfy the approach descrbed n the prevous secton, we present an evaluaton of the sze of changes n demographcal structures of European countres between the years 999 and 2000, usng the dscussed above coeffcents. The followng Tables and 2 contan values of ndcators evaluatng the change of demographcal structures for 27 countres between years 999 and 200; wth an ndcaton what poston they occuped n the rankng of values of ndvdual measures as well as two parttons of countres nto 4 groups (columns C and C2). The partton s made based on the values of ndcator M (arthmetc mean of values of ndcators R, C, J, D and T) and ndcator W, whle the thresholds were defned as: Ad, A, A+d, where A denotes an average and d standard devaton.
13 An applcaton of radar charts 9 Table. Values and rankngs of ndcators evaluatng the smlarty of demographcal structures of 27 European countres n the years 999 and 200. Indcators are defned on the grounds of formulas: R  (3), C  (6), J  (7), D  (8), T(0), M=(R+C+J+D+T)/5, W  () for the followng orderng of age ranges: 04, 524, 2549, 5064, 6579, >80. The last two columns contan nformaton about the partton nto 4 groups, accordng to values of ndcators M and W, respectvely. No. country R C J D T M W R C J D T M W C C2 Austra 0,9676 0,9536 0,90 0,9534 0,9762 0,9524 0, Belgum 0,966 0,9427 0,893 0,9425 0,9704 0,947 0, Bulgara 0,9455 0,9038 0,8243 0,9037 0,9494 0,9054 0, Cyprus 0,939 0,8967 0,820 0,8963 0,9453 0,8964 0, Czech Republc 0,9347 0,8776 0,788 0,8776 0,9348 0,883 0, Denmark 0,978 0,9606 0,9242 0,9606 0,9799 0,9607 0, Estona 0,9634 0,9438 0,8933 0,9437 0,970 0,9430 0, Fnland 0,9469 0,923 0,8385 0,92 0,9540 0,928 0, France 0,9504 0,980 0,8482 0,978 0,9572 0,983 0, Germany 0,9624 0,9340 0,8762 0,9340 0,9659 0,9345 0, Greece 0,9364 0,8900 0,806 0,8899 0,947 0,899 0, Hungary 0,944 0,8950 0,800 0,8950 0,9446 0,8978 0, Ireland 0,9225 0,8754 0,7779 0,875 0,9334 0,8769 0, Italy 0,9620 0,9346 0,877 0,9345 0,9662 0,9349 0, Latva 0,9587 0,9386 0,8839 0,9384 0,9682 0,9375 0, Lthuana 0,945 0,9239 0,8577 0,9234 0,9602 0,9220 0, Luxembourg 0,976 0,9650 0,938 0,9647 0,9820 0,9630 0, Malta 0,9263 0,8809 0,7867 0,8806 0,9365 0,8822 0, Netherlands 0,953 0,9276 0,8646 0,9274 0,9623 0,9270 0, Poland 0,906 0,8464 0,733 0,8460 0,966 0,8497 0, Portugal 0,9357 0,8873 0,7973 0,8872 0,9402 0,8895 0, Romana 0,9346 0,8820 0,7888 0,8820 0,9373 0,8849 0, Slovaka 0,93 0,853 0,7435 0,8529 0,9206 0,8566 0, Slovena 0,9288 0,8667 0,7647 0,8667 0,9286 0,87 0, Span 0,9299 0,8860 0,7949 0,8857 0,9394 0,8872 0, Sweden 0,9689 0,9594 0,925 0,9592 0,9792 0,9576 0, Unted Kngdom 0,9700 0,9625 0,9272 0,9622 0,9808 0,9605 0, Source: own work Note that each of the frst 5 ndcators presented n Table, has an dentcal geometrcal nterpretaton of smlarty of structures, an ntersecton of two hexagons that represent those structures. They dffer only by the method used to normalze that area, so that the value of the ndcator of smlarty s between [0, ]. That s why all the ndcators, wth the excepton of ndcator R, they gve the same orderng of European countres, accordng to the smlarty of structures for the years 999 and 200. Small dfferences are vsble only n the case of ndcator R. The results do not change f we modfy the ndcator so that ts value s ndependent of the orderng of coordnates of the vector representng the structure (see. Table 2). On the other hand, dfferences between the orderng by the value of ndcator W (based on a dfferent vsualzaton of structures that the rest), and the
14 0 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny orderng by the value of ndcator M are notceable. Even more so n the last two columns of Table 2, whch represent the partton of countres nto 4 groups, accordng to the smlarty of structures for years 999 and 200. In case of Span, we can observe a substantal dfference n the assgnment to a group dependng on the used ndcator. Table 2. Descrpton s smlar to that of Table. The calculatons of ndvdual ndcators where performed based on the frst formulas (maxmum) from (5), (3) and analogous modfcatons freeng the value of an ndcator from the orderng of coordnates of a vector descrbng a gven structure. No. country R M C M J M D M T M M M W R M C M J M D M T M M M W C C2 Austra 0,9737 0,9572 0,977 0,957 0,978 0,9567 0, Belgum 0,967 0,9427 0,893 0,9425 0,9704 0,9428 0, Bulgara 0,9658 0,9360 0,8796 0,9360 0,9669 0,9369 0, Cyprus 0,9592 0,9239 0,8575 0,9233 0,960 0,9248 0, Czech Republc 0,9582 0,926 0,8545 0,925 0,9592 0,9230 0, Denmark 0,982 0,9658 0,9338 0,9658 0,9826 0,9658 0, Estona 0,9702 0,952 0,9066 0,950 0,9749 0,9508 0, Fnland 0,9605 0,9294 0,8673 0,9290 0,9632 0,9299 0, France 0,9590 0,9234 0,8577 0,9234 0,9602 0,9247 0, Germany 0,9668 0,9386 0,8842 0,9385 0,9683 0,9393 0, Greece 0,9629 0,936 0,878 0,935 0,9646 0,9325 0, Hungary 0,9635 0,938 0,8722 0,937 0,9647 0,9328 0, Ireland 0,9665 0,9429 0,898 0,9428 0,9705 0,9429 0, Italy 0,9804 0,9669 0,9357 0,9668 0,983 0,9666 0, Latva 0,9632 0,946 0,8890 0,942 0,9697 0,940 0, Lthuana 0,9527 0,9254 0,8598 0,9246 0,9608 0,9247 0, Luxembourg 0,979 0,9650 0,938 0,9647 0,9820 0,9645 0, Malta 0,949 0,9097 0,8340 0,9095 0,9526 0,90 0, Netherlands 0,9653 0,9379 0,883 0,9379 0,9680 0,9384 0, Poland 0,9468 0,903 0,8233 0,903 0,949 0,905 0, Portugal 0,9680 0,9376 0,8826 0,9376 0,9678 0,9387 0, Romana 0,9548 0,972 0,8470 0,97 0,9568 0,986 0, Slovaka 0,9544 0,98 0,8378 0,98 0,9538 0,939 0, Slovena 0,9482 0,95 0,846 0,940 0,955 0,948 0, Span 0,9705 0,9425 0,893 0,9425 0,9704 0,9434 0, Sweden 0,984 0,9649 0,9322 0,9649 0,9822 0,965 0, Unted Kngdom 0,9790 0,9634 0,9293 0,9634 0,983 0,9633 0, Source: own work Tables and 2 show that the greatest stablty of the demographcal structure between 999 and 200 was possessed by: Austra, Denmark, Luxembourg, Sweden and Unted Kngdom. On the other hand, the greatest changes were observed n: Cyprus, Malta, Poland, Slovaka and Slovena. The greatest change occurred n Poland, and the smallest one n Luxembourg.
15 An applcaton of radar charts SUMMARY Means for defnng the values of ndcators of smlarty that use geometrcal nterpretatons n the form of a value of an area and are descrbed n ths work can also be used n other geometrcal ways of studyng the smlarty of structures as well as objects. These ways are an example of applyng geometrcal methods that are ntroduced by the authors usng radar charts [Bnderman, Borkowsk, Szczesny 2008, 200]. The emprcal analyss shows that when structures are not subject to large changes then the values of ndvdual ndcators, based on the same geometrcal nterpretaton, they order the structures smlarly. However, f we change the way of vsualzng the smlarty (the geometrcal nterpretaton) then we see changes n orderng. That s the reason why t s advsable to use several dfferent ndcators that use dfferent means of vsualzaton. Furthermore, t s worth notng that by usng geometrcal nterpretaton as a bass to construct an ndcator of smlarty we can obtan an ndcator that s very senstve to changes n the orderng of coordnates of a vector that numercally represents a gven structure. In practce there may be stuatons n whch a researcher desres such qualty n an ndcator so t may vsbly hghlght even small dfferences between structures, but for a gven orderng of ther components. However, one needs to remember that methods of constructng ndcators of smlarty that use a geometrcal nterpretaton are often appled manly because of the ease of vsualzaton of multdmensonal data. Then an unseasoned researcher may msuse them. It must be hghlghted that ndcators based solely on those llustratons do not satsfy often posed n the lterature on ths subject the basc requrement of stablty of the used method [see Jackson 970], that means the ndependence of the orderng of features. Technques presented by the authors show how a defnton of an ndcator must be modfed (the method of measurement) to remove ths flaw. Technques that were ponted out may seem numercally complex; nevertheless, n the age of computers that problem became nsgnfcant. On the other hand, ths smple and stable emprcal example shows that by applyng modfcatons, that s makng the measurement of smlarty ndependent of the orderng of ndvdual components of the structure, we obtan dfferent results (see Tables and 2, e.g., Span). The measurement of smlarty of structures based on geometrcal nterpretaton becomes even more complcated when a researcher s nterested n changes that occurred n a gven structures durng the whole studed perod and not only between the begnnng and the end of the sample. Further works on ths subject can be found n the work Bnderman and Szczesny 20.
16 2 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny REFERENCES Bnderman Z., Borkowsk B., Szczesny W. (2008) O pewnej metodze porządkowana obektów na przykładze regonalnego zróżncowana rolnctwa, Metody loścowe w badanach ekonomcznych, IX, wyd. SGGW, Bnderman Z., Borkowsk B., Szczesny W (2009) O pewnych metodach porządkowych w analze polskego rolnctwa wykorzystujących funkcje użytecznośc, Rocznk Nauk Rolnczych PAN, Sera G, Ekonomka Rolnctwa, T. 96, z. 2, Bnderman Z., Borkowsk B., Szczesny W. (2009a) Tendences n changes of regonal dfferentaton of farms structure and area Quanttatve methods n regonal and sectored analyss / sc. ed. D. Wtkowska D., Łatuszyńska M., U.S., Szczecn, Bnderman Z., Borkowsk B., Szczesny W. (200) Radar measures of structures conformablty, Quanttatve methods n economy, v. XI, No., Bnderman Z., Borkowsk B., Szczesny W. (200a) The tendences n regonal dfferentaton changes of agrcultural producton structure n Poland, Quanttatve methods n regonal and sectored analyss, U.S., Szczecn, Bnderman Z., Borkowsk B., Szczesny W. (200b) Wykorzystane metod geometrycznych do analzy regonalnego zróżncowana kultury na ws, Sera T. XII, z. 5, Bnderman, Z., Borkowsk B., Szczesny W. (200c) Regonalne zróżncowane turystyk w Polsce w latach , Oeconoma 9 (3) Bnderman Z., Borkowsk B., Szczesny W. (200d) Regonalnego zróżncowane kultury mędzy wsą a mastem w latach , Mędzy dawnym a nowym na szlakach humanzmu, wyd. SGGW, Bnderman Z., Szczesny W. (2009) Arrange methods of tradesmen of software wth a help of graphc representatons Computer algebra systems n teachng and research, Sedlce, Wyd. WSFZ, 73. Bnderman Z., Szczesny W., (20) Comparatve Analyss of Computer Technques for Vsualzaton Multdmensonal Data, Computer algebra systems n teachng and research, Sedlce, wyd. Collegum Mazova, Bnderman Z. (2009) Syntetyczne mernk elastycznośc przedsęborstw, Kwartalnk Prace Materały Wydzału Zarządzana Unwersytetu Gdańskego, nr 4/2, Bnderman, Z. (2009a) Ocena regonalnego zróżncowana kultury turystyk w Polsce w 2007 roku Rocznk Wydzału Nauk Humanstycznych, SGGW, T XII, Borkowsk B., Szczesny W. (2002) Metody taksonomczne w badanach przestrzennego zróżncowana rolnctwa. Warszawa, RNR, Sera G, T 89, z Breman L. (994) Baggng predctors, Techncal Report 420, Departament of Statstcs, Unversty of Calforna, CA, USA, September 994. Cok A., Kowalczyk T., Pleszczyńska E., Szczesny W. (995) Algorthms of grade correspondencecluster analyss. The Collected Papers on Theoretcal and Apled Computer Scence, 7, Deza E., Deza M.M. (2006) Dctonary of Dstances, Elsever. Dce Lee R. (945) Measures of the Amount of Ecologc Assocaton Between Speces, Ecology, Ecologcal Socety of Amerca, Vol. 26, No. 3,
17 An applcaton of radar charts 3 Duda R. O., Hart P. E., Stork D. G. (2000) Pattern Classfcaton. John Wley & Sons, Inc., 2nd ed. Gordon, A.D. (999) Classfcaton, 2nd edton, LondonNew York. Hubalek Z. (982) Coeffcents of Assocaton and Smlarty, Based on Bnary (Presence Absence) Data: An Evaluaton, Bologcal Revews, Vol.574, Jaccard P. (90) Étude comparatve de la dstrbuton florale dans une porton des Alpes et des Jura. Bulletn del la Socété Vaudose des Scences Naturelles 37, Jaccard, P. (902) Los de dstrbuton florale dans la zone alpne. Bull. Soc. Vaud. Sc. Nat. 38, Jaccard, P. (908) Nouvel les recherches sur la dstrbuton floral e. Bull. Soc. Vaud. Sc. Nat. 44, Jackson D. M. (970) The stablty of classfcatons of bnary attrbute data, Techncal Report 7065, Cornell Unversty, 3. Kukuła K. (2000) Metoda untaryzacj zerowej, PWN, Warszawa. Kukuła K. (red) (200) Statystyczne studum struktury agrarnej w Polsce, PWN, Warszawa. Legendre P., Legendre L. (998) Numercal Ecology, Second Englsh Edton Ed., Elsever. Malna A. (2004) Welowymarowa analza przestrzennego zróżncowana struktury gospodark Polsk według województw. AE, Sera Monografe nr 62, Kraków. Monev V. (2004) Introducton to Smlarty Searchng n Chemstry, MATCH Commun. Math. Comput. Chem. 5, Mostowsk A., Stark M.: Elementy algebry wyższej, PWN, Warszawa. Szczesny W. (2002) Grade correspondence analyss appled to contngency tables and questonnare data, Intellgent Data Analyss, vol. 6, 75. Tan P., Stenbach M., Kumar V. (2006) Introducton to Data Mnng, Pearson Educaton, Inc. Tanmoto, T.T. (957) IBM Internal Report 7th Nov. 957 Tanmoto T.T. (959) An Elementary Mathematcal Theory of Classfcaton and Predcton, IBM Program IBCFL. Tversky A. (957) Features of smlarty. Psychologcal Revew, 84(4) Warrens M. J. (2008) On Assocaton Coeffcents for 2 2 Tables and Propertes that do not depend on the Margnal Dstrbutons, Psychometrka Vol. 73, n. 4,
18 4 Zbgnew Bnderman, Bolesław Borkowsk, Wesław Szczesny
19 QUANTITATIVE METHODS IN ECONOMICS Vol. XII, No., 20, pp SOME REMARKS ON APLICATIONS OF ALGEBRAIC ANALYSIS TO ECONOMICS Zbgnew Bnderman, Marek Werzbck Department of Econometrcs and Statstcs Warsaw Unversty of Lfe Scences SGGW emals: Abstract: In ths paper, the author contnues the nvestgatons started n hs earler work [Bnderman 2009]. Here, problems of lnear equaton Dx=y wth the dfference operator D are studed. The work s an ntroducton to applcatons of the theory of rght nvertble operators to economcs. As an example, quotatons of KGHM on Warsaw Stock Exchange are consdered. Key words: algebrac analyss, rght nvertble operator, dfference operator, quotatons of Stock Exchange, Jacoban matrx In memory of Professor Krystyna Twardowska INTRODUCTION In mathematcs the term Algebrac Analyss s used n two completely dfferent senses [cf. Przeworska  Rolewcz 2000]. Here, meanng of Algebrac Analyss s closely connected wth theory of rght nvertble operators [cf. Przeworska  Rolewcz 988]. In the earler work of the author [Bnderman 2009] a new defnton of elastcty operators n algebras wth rght nvertble operators was proposed. The defnton uses logarthmc mappngs of algebrac analyss [cf. PrzeworskaRolewcz 998]. The obtaned results were appled to economcs n order to fnd a functon f elastcty of ths functon s gven. Here, possbltes of applcatons of algebrac analyss to economcs, on the smple example of the dfference operator D and the lnear equaton Dx=y are presented. The paper s an ntroducton n ths range.
20 6 Zbgnew Bnderman, Marek Werzbck Throughout ths work wll denote ether the real feld,, or the complex feld, Let X and Y be a lnear space over. The set of all lnear operators domans contaned n X and ranges contaned n Y wll be denoted by L(X,Y). We shall wrte: L0(X,Y): = { A L(X,Y):domA = X }, L(X): = L(X,X), L0(X) : = L0(X, X), ker A :{ x dom A :Ax = 0} for A L(X, Y). Followng D. Przeworska  Rolewcz [c.f. Przeworska  Rolewcz 988], an operator D L(X) s sad to be rght nvertble f there s an operator R L L 0 (X) such that RX dom D and DR=I. The operator R s called a rght nverse of D. We shall consder n L(X) the followng sets: the set R(X) of all rght nvertble operators belongng to L(X) ; the set R D := { R L 0 (X) : DRx = x for all x X }; the set F D := { F L 0 (X) : F 2 = F, FX = ker D and R R D : FR=0} of all ntal operators for a D R(X). We note, f D R(X), R R D and ker D {0 }, then the operator D s rght nvertble, but not nvertble. We have DRx= x for all x X and x dom D: RDx x. Here, the nvertblty of an operator A L (X) means that the equaton Ax=y has the unque soluton for every y X. If D R(X) and 0 z ker D and x s a soluton of the equaton DX=y then the element x +z s also the soluton of ths equaton. If F s an ntal operator for D correspondng to R then Fx =x RDx=(IRD)x for x dom D and Fz=z for z ker D. () We note, a dfferent approach to the defnton of rght nvertble lnear operators s presented n the work [Bnderman 2009]. In the sequel we shall assume that D R(X), R R D, F F D s an ntal operator for D correspondng to R and dm ker D>0,.e. D s rght nvertble but not nvertble. We observe, that f we know one rght nverse of D then the sets [c.f. Przeworska  Rolewcz 988] R D = {R + FA: A L 0 (X)}; (2) F D = {F(IAD): A L 0 (X)}. (3) We shall need the two followng theorems [c.f. Przeworska  Rolewcz 988]. Theorem. The general soluton of the equaton s gven by the formula Dx = y, y X, (4)
METODY ILOŚCIOWE W BADANIACH EKONOMICZNYCH
Warsaw Unversty of Lfe Scences SGGW Faculty of Appled Informatcs and Mathematcs METODY ILOŚCIOWE W BADANIACH EKONOMICZNYCH QUANTITATIVE METHODS IN ECONOMICS Volume XII, No. EDITORINCHIEF Bolesław Borkowsk
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationScale Dependence of Overconfidence in Stock Market Volatility Forecasts
Scale Dependence of Overconfdence n Stoc Maret Volatlty Forecasts Marus Glaser, Thomas Langer, Jens Reynders, Martn Weber* June 7, 007 Abstract In ths study, we analyze whether volatlty forecasts (judgmental
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationThe covariance is the two variable analog to the variance. The formula for the covariance between two variables is
Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More information1 Example 1: Axisaligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationAbstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING
260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationForecasting Irregularly Spaced UHF Financial Data: Realized Volatility vs UHFGARCH Models
Forecastng Irregularly Spaced UHF Fnancal Data: Realzed Volatlty vs UHFGARCH Models FrançosÉrc Raccot *, LRSP Département des scences admnstratves, UQO Raymond Théoret Département Stratége des affares,
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationRing structure of splines on triangulations
www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAMReport 201448 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationRisk Model of LongTerm Production Scheduling in Open Pit Gold Mining
Rsk Model of LongTerm Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationBinomial Link Functions. Lori Murray, Phil Munz
Bnomal Lnk Functons Lor Murray, Phl Munz Bnomal Lnk Functons Logt Lnk functon: ( p) p ln 1 p Probt Lnk functon: ( p) 1 ( p) Complentary Log Log functon: ( p) ln( ln(1 p)) Motvatng Example A researcher
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationMAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPPATBDClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationThe Impact of Stock Index Futures Trading on Daily Returns Seasonality: A Multicountry Study
The Impact of Stock Index Futures Tradng on Daly Returns Seasonalty: A Multcountry Study Robert W. Faff a * and Mchael D. McKenze a Abstract In ths paper we nvestgate the potental mpact of the ntroducton
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationCalendar Corrected Chaotic Forecast of Financial Time Series
INTERNATIONAL JOURNAL OF BUSINESS, 11(4), 2006 ISSN: 1083 4346 Calendar Corrected Chaotc Forecast of Fnancal Tme Seres Alexandros Leonttss a and Costas Sropoulos b a Center for Research and Applcatons
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationMacro Factors and Volatility of Treasury Bond Returns
Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationPRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB.
PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. INDEX 1. Load data usng the Edtor wndow and mfle 2. Learnng to save results from the Edtor wndow. 3. Computng the Sharpe Rato 4. Obtanng the Treynor Rato
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationThe eigenvalue derivatives of linear damped systems
Control and Cybernetcs vol. 32 (2003) No. 4 The egenvalue dervatves of lnear damped systems by YeongJeu Sun Department of Electrcal Engneerng IShou Unversty Kaohsung, Tawan 840, R.O.C emal: yjsun@su.edu.tw
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2  Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of noncoplanar vectors Scalar product
More informationHigh Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)
Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationWorld currency options market efficiency
Arful Hoque (Australa) World optons market effcency Abstract The World Currency Optons (WCO) maket began tradng n July 2007 on the Phladelpha Stock Exchange (PHLX) wth the new features. These optons are
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationGender differences in revealed risk taking: evidence from mutual fund investors
Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationTransition Matrix Models of Consumer Credit Ratings
Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss
More informationFREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES
FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EKMUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan
More informationMarginal Returns to Education For Teachers
The Onlne Journal of New Horzons n Educaton Volume 4, Issue 3 MargnalReturnstoEducatonForTeachers RamleeIsmal,MarnahAwang ABSTRACT FacultyofManagementand Economcs UnverstPenddkanSultan Idrs ramlee@fpe.ups.edu.my
More informationTwo Faces of IntraIndustry Information Transfers: Evidence from Management Earnings and Revenue Forecasts
Two Faces of IntraIndustry Informaton Transfers: Evdence from Management Earnngs and Revenue Forecasts Yongtae Km Leavey School of Busness Santa Clara Unversty Santa Clara, CA 950530380 TEL: (408) 5544667,
More informationComparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions
Comparson of Control Strateges for Shunt Actve Power Flter under Dfferent Load Condtons Sanjay C. Patel 1, Tushar A. Patel 2 Lecturer, Electrcal Department, Government Polytechnc, alsad, Gujarat, Inda
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationTourism and trade in OECD countries. A dynamic heterogeneous panel data analysis
Toursm and trade n OECD countres. A dynamc heterogeneous panel data analyss María SantanaGallego a, Francsco LedesmaRodríguez a, Jorge V. PérezRodríguez b* a Facultad de Cencas Económcas y Empresarales,
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More information2.4 Bivariate distributions
page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together
More informationLogistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification
Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson
More informationPERRON FROBENIUS THEOREM
PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()
More informationGRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 NORM
GRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 NORM BARRIOT JeanPerre, SARRAILH Mchel BGI/CNES 18.av.E.Beln 31401 TOULOUSE Cedex 4 (France) Emal: jeanperre.barrot@cnes.fr 1/Introducton The
More informationSTATISTICAL DATA ANALYSIS IN EXCEL
Mcroarray Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 6 Some Advanced Topcs Dr. Petr Nazarov 1401013 petr.nazarov@crpsante.lu Statstcal data analyss n Ecel. 6. Some advanced topcs Correcton for
More informationDamage detection in composite laminates using cointap method
Damage detecton n composte lamnates usng contap method S.J. Km Korea Aerospace Research Insttute, 45 EoeunDong, YouseongGu, 35333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The contap test has the
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More information