Negative moments of a modified power series distribution and bias of the maximum likelihood estimator |
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Authors: | Ashish Kumar P.C. Consul |
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Affiliation: | University of Calgary , Calgary, Alberta, Canada |
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Abstract: | The class of Modified Power Series distributions (MPSD) containing Lagrangian Poisson (LPD) (Consul and Jain, 1973) and Lagrangian binomial distributions (LBD) (Jain and Consul, 1971) was studied by Gupta (1974). We investigate the problem of finding the negative momentsE[X-r ], of displaced and decapitated Modified Power Series Distributions. We derive the relationship between rand (r-1) negative moments. The negative moments of the decapitated and displaced LPD are obtained. These results are, then, used to find the exact amount of bias in the ML estimators of the parameters in the LPD and the LBD. We have also given the variances of the ML estimator and the minimum variance unbiased estimator of the parameter in the LPD. |
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Keywords: | Maximum Likelihood Estimate Modified Power Series distribution bias negative moments Lagrangian Poisson distribution Lagrangian binomial distribution |
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