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Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

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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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Authors and Affiliations

  1. Unitat d'Estadistica i Investigació, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

    Joan Del Castillo & Pedro Puig

Authors
  1. Joan Del Castillo
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  2. Pedro Puig
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Del Castillo, J., Puig, P. Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions. Annals of the Institute of Statistical Mathematics 49, 255–269 (1997). https://doi.org/10.1023/A:1003158828665

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  • DOI: https://doi.org/10.1023/A:1003158828665

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