Goodness-Of-Fit For The Generalized Exponential Distribution

by Amal, S. Hassan.

Abstract: Distribution called generalized exponential or exponentiated exponential distribution was introduced and studied quite extensively by the authors (see Gupta and Kundu, 1999, 2001a, 2001b, 2002, 2003). A class of goodness-of-fit tests for the generalized exponential distribution with estimated parameter is proposed. The tests are based on the empirical distribution function. These test statistics are available when the hypothesized distribution is completely specified. When the parameters of the generalized exponential distribution are not known and must be estimated from the sample data, the standard Tables for these test statistics are not valid. This article uses Monte Carlo and Pearson system techniques to create Tables of critical values for such situations. Moreover, the power of the proposed test statistics is investigated for a number of alternative distributions. The results of the power studies showed that the test statistic proposed by Liao and Shimokawa (1999) is the most powerful goodness-of-fit test among the competitors.

Key Words: Anderson-Darling test statistic, Cramer–von Mises test statistic, Kolmogorov-Smirnov statistic, Watson statistic, Critical values, Generalized exponential distribution, Power test

Author:
Amal, S. Hassan, amal52_soilman @yahoo.com

Editor: Meintanis,Simos G.,simosmei@econ.uoa.gr

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