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Biometrika 1983 70(2):479-484; doi:10.1093/biomet/70.2.479
© 1983 by Biometrika Trust
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MISCELLANEA

Some methods of estimation for the bivariate Hermite distribution

H. PAPAGEORGIOU, C. D. KEMP and S. LOUKAS

Statistical Unit, University of Athens Greece
School of Mathematical Sciences, University of Bradford
Department of Mathematics, University of loannina Greece

Maximum likelihood estimation of bivariate Hermite parameters is awkward in that it requires iteration techniques which are complicated and relatively time-consuming even on modern computers. In the present paper we study several alternative estimation procedures which lead to explicit expressions for the parameter estimates in terms of fairly simple sample statistics. Asymptotic efficiencies are examined and recommendations made. For comparison, three simple methods are applied to the accident data set which Kemp & Papageorgiou (1982) used to illustrate the maximum likelihood method.

Key Words: Accident data • Asymptotic efficiency • Bivariate Hermite distribution • Estimation • Method of even points • Method of moments • Method of zero frequencies


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