ON ESTIMATING THE PARAMETER OF A TRUNCATED GEOMETRIC DISTRIBUTION.
Themis Signal Analysis Statistics Research Program,
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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The paper is concerned with the problem of maximum likelihood estimation for the parameter, of the geometric distribution, from samples which are truncated at arbitrary points in either or both tails of the distribution. It is shown that the maximum likelihood estimator is the solution of a polynomial of high degree, and a table is given for solving the maximum likelihood estimating equation. The derivation of the asymptotic variance of the estimator is presented and the result is used in the study of the asymptotic efficiency of the estimation in truncated sampling. The efficiency of the maximum likelihood estimator for complete samples is derived and it is shown that the estimator based on truncated samples always provide less information about the parameter than that based on complete sample of the same size. Author
- Statistics and Probability