QUADRATIC DISTANCE ESTIMATORS FOR THE ZETA-FAMILY

The zeta distribution is a discrete distribution which has been relati vely little used in actuarial science and statistics, a reason being t hat most estimators proposed in the literature for the parameter of th is distribution require iterative methods or the extensive use of tabl es for its calculation, due to the complicated form of its probability mass function. In this paper, we propose a new estimator, based on qu adratic distance, asymptotically fully efficient for parameter values greater than 2 and highly efficient for smaller values, but computatio nally more appealing than the maximum likelihood estimator; we also co mpare its asymptotic variance with that of the moment estimator and th e estimator based on the ratio of the observed frequencies of the firs t two classes.