Anderson–Darling statistic and its inverse

8^th International Conference and Exhibition on Lasers, Optics & Photonics

November 15-17, 2017 | Las Vegas, USA

Gennady Martynov

Russian Academy of Sciences, Russia

Posters & Accepted Abstracts: J Laser Opt Photonics

Abstract :

For more than 60 years, Anderson-Darling statistic is one of the most popular in applications among the Cram�©r-von-Mises goodness-of-fit tests. This statistic modifies the classical empirical process in the interval [0, 1] by multiplying it by a weighting function . The weighting function redistributes the test sensitivity to deviations of the alternative distribution function from the hypothetical on different subsets of [0.1]. In practice, the tests can be of interest having other weight functions. The paper proposes new formulas for eigen functions of the Anderson-Darling statistics. Also, it was analyzed as statistic "inverse" to the Anderson-Darling statistic with the weighting function . This was considered also as another weighting function. The proposed theory is based on the use of various special functions. In practice, it could be useful for the Cram�©r-vonMises tests with weighting functions from the family , �±>-1, �²>-1. The paper contains a table of distribution for these statistics with different values of the degrees �±>1 and �²>-1.$ The table was calculated by different methods with good precision without using the statistical simulation.