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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