Complete sufficiency and maximum likelihood estimation for the two-parameter negative binomial distribution |
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Authors: | L. J. Willson J. L. Folks J. H. Young |
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Affiliation: | 1. Department of Statistics, Oklahoma State University, 74078, Stillwater, Oklahoma 2. Department of Entomology, Oklahoma State University, 74078, Stillwater, Oklahoma
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Abstract: | The difficult estimation problem associated with the two-parameter negative binomial distribution is discussed. The order statistic is shown to be minimal sufficient but not complete. It is proven that there is at least one maximum likelihood estimator of the parameterk when the second sample moment is greater than the sample mean. Contours and three-dimensional graphs of the natural logarithm of the likelihood function provide further insight into the estimation problem. |
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