Advanced Statistical Methods in Insurance

Size: px

Start display at page:

Download "Advanced Statistical Methods in Insurance"

Lambert Rose
8 years ago
Views:

1 Advanced Statistical Methods in Insurance 7. Multivariate Data All Pairwise Scattergrams Iris Data Set: 3 Species 50 Cases of each with p=4 measurements per case 2 Hudec & Schlögl 1

2 3-d Scatterplots iris[, 1] iris[, 1] iris[, 3] iris[, 2] iris[, 3] iris[, 2] 3 Hudec & Schlögl Visualization of 4 variables in a Scatterplot Vars define position 2 Vars define shape 4 Hudec & Schlögl 2

variables in a Scatterplot 5 3.0 3.5 4.0 4.5 2.0 2.

3 Conditioning Plots Cleveland, W. S. (1993) [ ] [ Hudec & Schlögl Conditioning Variable Plots i4 i4 i4 i4 i4 i4 Use 4 th Variable for Conditioning 6 Hudec & Schlögl 3

4 Parallel Plots (Profile Plots) Species Petal.Width Petal.Length Sepal.Width Sepal.Length Min 7 Hudec & Schlögl Max Conditioned Parallel Plots (Profile Plots) Petal.Width virginica Petal.Length Sepal.Width Sepal.Length Petal.Width Petal.Length th Sepal.Width Sepal.Length setosa versicolor Min Max 8 Hudec & Schlögl 4

5 Andrews Curves a1 = 1/ 2 p j f i(t) = a j(t) x sin( t) for j = 2, 4, K ij 2 a j = j= 1 j 1 cos( t) for j = 3,5, K 2 9 Hudec & Schlögl Chernoff-Faces Hudec & Schlögl 5

6 Glyphs Multiple-symbol Approach 11 Hudec & Schlögl Cars Database Manufacturer Model Type Min.Price Price Max.Price MPG.city MPG.highway AirBags DriveTrain 1 Acura Integra Small None Front 2 Acura Legend Midsize Driver & Passenger Front 3 Audi 90 Compact Driver only Front 4 Audi 0 Midsize Driver & Passenger Front 5 BMW 535i Midsize Driver only Rear 6 Buick Century Midsize Driver only Front Cylinders EngineSize Horsepower RPM Rev.per.mile Man.trans.avail Fuel.tank.capacity Passengers Length Yes Yes Yes Yes Yes No Wheelbase Width Turn.circle Rear.seat.room Luggage.room Weight Origin Make non-usa Acura Integra non-usa Acura Legend non-usa Audi non-usa Audi non-usa BMW 535i USA Buick Century 12 Hudec & Schlögl 6

6 19 26 Driver & Passenger Front 5 BMW 535i Midsize 23.7 30.0 36.2 22 30 Driver only Rear 6 Buick Century Midsize 14.2 15.7 17.3 22 31 Driver only Front Cylinders EngineSize Horsepower RPM Rev.per.

7 in.pric Price ax.pric PG.ci G.high 20 1 ginesi rsepow RPM v.per.m 1500 ank.ca ssenge Length heelba Width rn.circ.seat.r gage.r Weigh Hudec & Schlögl Wheelbase Length Weight Fuel.tank.capacity Width EngineSize Turn.circle Price Min.Price Max.Price Horsepower Luggage.room Rear.seat.room Passengers MPG.highway MPG.city Rev.per.mile RPM RPM Rev.per.mile MPG.city MPG.highway Passengers Rear.seat.room Luggage.room Horsepower Max.Price Min.Price Price Turn.circle EngineSize Width Fuel.tank.capacity Weight Length Wheelbase 14 Hudec & Schlögl 7

room Rear.seat.room Passengers MPG.highway MPG.city Rev.per.

8 3d-Visualisation of Functions f(x, y) wireframe(funval~grid[,1]*grid[,2], col=2, drape=t, xlab="", ylab="",zlab="", at=quantile(funval, 0:24/25), col.regions=heat.colors(25), par.settings=list(box.3d=f)) 15 Hudec & Schlögl Left: contourplot(funval~grid[,1]*grid[,2], cuts=20, col="blue ) Right: levelplot(funval~grid[,1]*grid[,2],cuts=20,col.regions=heat.colors(25)) Hudec & Schlögl 8

settings=list(box.3d=f)) 15 Hudec & Schlögl 0.04 002 0.02 0.16 0.14 8 6 0.09 0.01 002 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 0.11 0. 0.11 0.12 0.

Graphical Representation of Multivariate Data

Graphical Representation of Multivariate Data One difficulty with multivariate data is their visualization, in particular when p > 3. At the very least, we can construct pairwise scatter plots of variables.