Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions |
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Authors: | Joan Del Castillo Pedro Puig |
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Affiliation: | (1) Unitat d'Estadistica i Investigació, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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Abstract: | This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced. |
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Keywords: | Exponential families Gamma Rayleigh and singly truncated normal distributions |
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