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Biometrika 1982 69(2):467-472; doi:10.1093/biomet/69.2.467
© 1982 by Biometrika Trust
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Asymptotic efficiencies of three methods of estimation for the inverse Gaussian-Poisson distribution

H. S. STCHKL

Faculty of Industrial Engineering and Management Technion, Haifa, Israel

The two parameters of the inverse Gaussian-Poisson distribution may be estimated by (a) sample moments, (b) the proportion of zeros and the mean in the sample, and (c) by maximum likelihood. In the paper the asymptotic variances for all three joint estimation techniques and the corresponding efficiencies for methods (a) and (b) are derived. For {theta} ≥ 0.90 and {alpha} ≤ 1.5, the simple method (b) is highly efficient whereas the moment estimators are clearly inefficient. For 1.5 < {alpha} < 20.0 and {theta} ≥ 0. 90, both methods (a) and (b) are very inefficient and the maximum likelihood estimation technique should be employed.

Key Words: Asymptotic efficiency • Inverse Gaussian-Poisson distribution • Maximum likelihood estimation • Moment estimation • Proportion of zeros


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