Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions

Abstract

An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution functions corresponding to all observations. To overcome this drawback, the modified Anderson-Darling test was suggested by Ahmad et al. (1988b). In this study, the critical values of the modified Anderson-Darling test statistics are revised using simulation experiments with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance of the modified Anderson-Darling test. The results of the power study show that the modified Anderson-Darling test is more powerful than traditional tests such as the v 2 , Kolmogorov-Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the modified Anderson-Darling test is applied to the annual maximum rainfall data in Korea.

Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

“…However, while the null hypothesis of the KS test does not depend upon the explicit form of the distribution under analysis, the null hypothesis of the Lilliefors depends on the values of the shape parameter. Accordingly, the critical values for the Lilliefors test are usually derived from statistical simulations procedures (Shin et al, 2012;Heo et al, 2013;Blain, 2014). Further information on the Lilliefors test can be found in studies such as Blain (2014).…”

Climate trends in the municipality of Pelotas, state of Rio Grande do Sul, Brazil

“…In relation to the extreme values statistics, the AD test relies on the sum of squares of differences between theoretical and empirical distributions and on a weight function [Ψ(. )]), which gives greater emphasis, compared to KSL, to discrepancies in both ends (tails) of the respective c urves (SHIN et al, 2012).…”

“…Thus it is necessary to use a Ψ(.) function capable of separately emphasize discrepancies in the upper and lower tails of the probability curves (SHIN et al, 2012). Ahmad et al (1988) …”

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

“…Regarding extreme-value statistics, the Anderson-Darling (AD) test (equation 4) is based on the sum of the squares of the differences between theoretical and empirical distribution with a weight function [Ψ(SPI)] which emphasizes the discrepancies in both upper and lower tails (SHIN et al, 2012). This last feature cannot be observed in the KS-L algorithm.…”

“…This last feature cannot be observed in the KS-L algorithm. According to SHIN et al (2012) the AD test is a powerful test because it emphasizes the tails differences. However, one may correctly argue that equation 4 gives equal weights to both upper and lower tails of the distribution (SHIN et al, 2012).…”