Abstract #302138

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JSM 2003 Abstract #302138
Activity Number: 338
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Education
Abstract - #302138
Title: The Distribution of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling Test Statistics for Exponential Populations with Estimated Parameters
Author(s): Diane L. Evans*+
Companies: Rose-Hulman Institute of Technology
Address: 7248 Belfonte Ln., Terre Haute, IN, 47802-9196,
Keywords: distribution functions ; goodness-of-fit test ; maximum likelihood estimation ; order statistics ; transformation technique
Abstract:

Although the Kolmogorov-Smirnov test statistic is easy to calculate, its distribution is mathematically intractable. Drew et al. provide an algorithm for calculating the CDF of the K-S test statistic when all the parameters of the hypothetical CDF are known (referred to as the "all parameters known" case). The more common and practical situation occurs when the parameters are unknown and are estimated from the sample data, using an estimation technique such as maximum likelihood. In this case, the distribution of the K-S test statistic depends upon both the sample size of the data and the particular distribution that is being fit to the data. This talk presents the derivation of the distribution of the K-S test statistic in the case of exponential sampling for n = 1 and n = 2. Additionally, the distribution of the Cramer-von Mises and Anderson-Darling test statistics are included.

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