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Biometrika 1982 69(2):391-399; doi:10.1093/biomet/69.2.391
© 1982 by Biometrika Trust
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A test of separate families of distributions based on the empirical moment generating function

T. W. EPPS1, K. J. SINGLETON2 and L. B. PULLEY3

1Department of Economics, University of Virginia Charlottesville, Virginia, U.S.A
2Graduate School of Industrial Administration, Carnegie-Mellon University Pittsburgh, Pennsylvania, U.S.A
3Department of Economics, Brandeis University Waltham, Massachusetts, U.S.A

In testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply. We propose a test based on the difference between the sample moment generating function and its theoretical counterpart under Ho. The argument of the moment generating function is chosen to maximize the test's large-sample power. Small-sample properties of the test in two applications are studied by simulation.

Key Words: Empirical characteristle function • Exponential distribution • Goodness-of-fit test • Likelihood ratio test • Log normal distribution • Neyman's type A distribution • Poisson distribution


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