A1160
Title: On modified Anderson-Darling statistic for various distributions with unknown parameters
Authors: Hidetoshi Murakami - Tokyo University of Science (Japan) [presenting]
Hikaru Yamaguchi - Tokyo University of Science (Japan)
Abstract: For a long time, numerous goodness-of-fit test statistics have been considered and applied in many scientific fields. One of the most powerful statistics is the Anderson-Darling statistic, which is sensitive to discrepancies at the tails of the distribution rather than near the center. However, for example, hydrologists are interested in estimates of flood magnitudes for high return periods. In these cases, the curiosity is concentrated on the upper tail of the distribution. Then, The aim is to propose the generalized modified Anderson-Darling statistic that emphasizes the upper or lower tails of the distribution. The limiting distribution of the proposed statistic is estimated by using both theoretical approximation and simulation. Under the finite sample sizes, the distribution of the proposed statistic is estimated via a simulation study. Simulations are used to investigate the power of proposed statistics for various distributions with unknown parameters. The proposed statistic is illustrated by the analysis of real data.
