### Abstract

Studies of the goodness-of-fit test, which describes how well a model fits a set of observations with an assumed distribution, have long been the subject of statistical research. The selection of an appropriate probability distribution is generally based on goodness-of-fit tests. This test is an effective means of examining how well a sample data set agrees with an assumed probability distribution that represents its population. However, the empirical distribution function test gives equal weight to the differences between the empirical and theoretical distribution functions corresponding to all observations. The modified Anderson-Darling test, suggested by Ahmad et al. (1988), uses a weight function that emphasizes the tail deviations at the upper or lower tails. In this study, we derive new regression equation forms of the critical values for the modified Anderson-Darling test statistics considering the effect of unknown shape parameters. The regression equations are derived using simulation experiments for extreme value distributions such as the log-Gumbel, generalized Pareto, GEV, and generalized logistic models. In addition, power test and at-site frequency analyses are performed to evaluate the performance and to explain the applicability of the modified Anderson-Darling test.

Original language | English |
---|---|

Pages (from-to) | 41-49 |

Number of pages | 9 |

Journal | Journal of Hydrology |

Volume | 499 |

DOIs | |

Publication status | Published - 2013 Aug 30 |

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### All Science Journal Classification (ASJC) codes

- Water Science and Technology

### Cite this

*Journal of Hydrology*,

*499*, 41-49. https://doi.org/10.1016/j.jhydrol.2013.06.008

}

*Journal of Hydrology*, vol. 499, pp. 41-49. https://doi.org/10.1016/j.jhydrol.2013.06.008

**Approximation of modified Anderson-Darling test statistics for extreme value distributions with unknown shape parameter.** / Heo, Jun-Haeng; Shin, Hongjoon; Nam, Woosung; Om, Juseong; Jeong, Changsam.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation of modified Anderson-Darling test statistics for extreme value distributions with unknown shape parameter

AU - Heo, Jun-Haeng

AU - Shin, Hongjoon

AU - Nam, Woosung

AU - Om, Juseong

AU - Jeong, Changsam

PY - 2013/8/30

Y1 - 2013/8/30

N2 - Studies of the goodness-of-fit test, which describes how well a model fits a set of observations with an assumed distribution, have long been the subject of statistical research. The selection of an appropriate probability distribution is generally based on goodness-of-fit tests. This test is an effective means of examining how well a sample data set agrees with an assumed probability distribution that represents its population. However, the empirical distribution function test gives equal weight to the differences between the empirical and theoretical distribution functions corresponding to all observations. The modified Anderson-Darling test, suggested by Ahmad et al. (1988), uses a weight function that emphasizes the tail deviations at the upper or lower tails. In this study, we derive new regression equation forms of the critical values for the modified Anderson-Darling test statistics considering the effect of unknown shape parameters. The regression equations are derived using simulation experiments for extreme value distributions such as the log-Gumbel, generalized Pareto, GEV, and generalized logistic models. In addition, power test and at-site frequency analyses are performed to evaluate the performance and to explain the applicability of the modified Anderson-Darling test.

AB - Studies of the goodness-of-fit test, which describes how well a model fits a set of observations with an assumed distribution, have long been the subject of statistical research. The selection of an appropriate probability distribution is generally based on goodness-of-fit tests. This test is an effective means of examining how well a sample data set agrees with an assumed probability distribution that represents its population. However, the empirical distribution function test gives equal weight to the differences between the empirical and theoretical distribution functions corresponding to all observations. The modified Anderson-Darling test, suggested by Ahmad et al. (1988), uses a weight function that emphasizes the tail deviations at the upper or lower tails. In this study, we derive new regression equation forms of the critical values for the modified Anderson-Darling test statistics considering the effect of unknown shape parameters. The regression equations are derived using simulation experiments for extreme value distributions such as the log-Gumbel, generalized Pareto, GEV, and generalized logistic models. In addition, power test and at-site frequency analyses are performed to evaluate the performance and to explain the applicability of the modified Anderson-Darling test.

UR - http://www.scopus.com/inward/record.url?scp=84880605994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880605994&partnerID=8YFLogxK

U2 - 10.1016/j.jhydrol.2013.06.008

DO - 10.1016/j.jhydrol.2013.06.008

M3 - Article

VL - 499

SP - 41

EP - 49

JO - Journal of Hydrology

JF - Journal of Hydrology

SN - 0022-1694

ER -