## Abstract

The generalized Poisson distribution (GPD), studied by many researchers and containing two parameters θ and A, has been found to fit very well data sets arising in biological, ecological, social and marketing fields. Consul and Shoukri (1985) have shown that for negative values of A the GPD gets truncated and the model becomes deficient; however, the truncation error becomes less than 0.0005 if the minimum number of non zero probability classes ≥4 for all values of 8 and A and the GPD model can be safely used in all such cases. The problem of admissible maximum likelihood (ML) estimation when the sample mean is larger than the sample variance is considered in this paper which complements the earlier work of Consul and Shoukri (1984) on the existence of unique ML estimators of θ and A when the sample mean is smaller than or equal to the sample variance.

Original language | English |
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Pages (from-to) | 299-309 |

Number of pages | 11 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1988 |

## Keywords

- admissible ML estimator
- likelihood equation
- uniqueestimators