# MORE ADEQUATE PROBABILITY DISTRIBUTIONS TO REPRESENT THE SATURATED SOIL HYDRAULIC CONDUCTIVITY 1,2

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4 792 Mesquita et al. Número de Observações Number of Odservations Lognormal Distribution ,00 0,02 0,04 0,06 0,08 0,10 0,12 Classes of Frequencie Número Number de of Observações Odservations 4 Gama Distribution ,00 0,02 0,04 0,06 0,08 0,10 0,12 Classes of Frequencie Figure 1 - (a) Lognormal and (b) Gamma Frequency Histograms and Probability Curves for the Ksat variable, (10-2 m s -1 ), Typic Hapludox (LVAd). 0,07 QQ Plot - Ksat - Lognormal Distribution 0,07 QQ Plot - Ksat - Gamma Distribution 0,06 0,06 Observed ed Values 0,0 0,04 0,03 0,02 0,01 Observed ed Values 0,0 0,04 0,03 0,02 0,01 0,00 0,00-0,01-0, Lognormal Quantiles Gamma Quantiles Figure 2 - (a) Lognormal Distribution and (b) Gamma Distribution Adjustment Chart for the Ksat variable, (10-2 m s -1 ), Typic Hapludox (LVAd). the set of utilized criteria, Kolmogorov-Smirnov, graphical, and by robust techniques, establishes without question the superiority of the lognormal distribution under these statistical criteria. In addition, the fit function depends on the precision of estimation of parameters α e β, which are directly linked to the shape of distribution of the observed values; this makes the gamma distribution difficult to use. The occurrence of soil properties with nonnormal distribution is common, and statistical procedures have been applied without the complete attention required by their foundation and limitations (Menk & Nagai, 1983). Many times, data are accepted as being normally distributed without appropriate questioning. In the present case, it would be equivalent to accepting the mean, median and standard deviation values presented in Table 1, which were obtained based on the normal distribution, but since the observed Ksat data are not normally distributed, those values cannot be used; otherwise they can lead to errors in the formulated conclusions. Parkin et al. (1988) and Parkin & Robinson (1992), evaluating sample data estimation methods for a lognormal population, concluded that the UMVUE method yields estimates with least errors. By this method, the characteristic values observed for Ksat, considering them lognormally distributed, are: mean x 10-2 m s -1, median x 10-2 m s -1, standard deviation x 10-2 m s -1, coefficient of variation 73%, lower and upper limits for the confidence interval of the mean (9%) x 10-2 m s -1 and x 10-2 m s -1, respectively. These parameters should then be analyzed, and utilized in the future as statistical parameters for the variable. If the sampling values are lognormally distributed we must choose, among the position parameters (mean and median), the one which is to be used as a statistical summary, because the values are not the same and

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