Many ratio type estimators for population mean have come into play in the past. Researchers over the years have been making efforts to improve the efficiency of thee estimators. There has been a lot of modification of some of these estimators. Some forms of comparison have been done in the literature. There is need to further compare these estimators with other existing estimators at varying sample sizes and also considering discrete and continuous distribution. Thirty-eight estimators, five different sample sizes and seven distributions were considered. The population mean estimates and their Bias were computed for the thirty- eight estimators at varying sample sizes under various distribution. The efficiency of the estimator was computed using Mean Square Error (MSE). Using simulation study, it was observed that the efficiency of the estimators increase as sample sizes increases and the estimator performed alike in most distributions
An Empirical Study on Modified Maximum Likelihood Estimator and Maximum Likelihood Estimator for Inverse Weibull Distribution by Using Type Ii Censored Sample (Review Completed - Accepted)
Parameter estimation become complicated when censoring is present in the sample Some time it is not possible to give a mathematical expression of estimated values of parameters in Maximum Likelihood (ML) method. .Dayyeh and Sawi (1996) used the Mehrotra and Nanda (1974) MML technique. They replaced the intractable term of likelihood equations with its expectation, to get the estimators of location parameter by considering the scale parameter equal to 1 of logistic distribution in right Type ll censored sample. Kambo (1978) derived the explicit solution for ML estimator of two parameter exponential distribution in the case of doubly type ll censored sample. In this paper MML estimator and ML estimator of inverse weibull distribution by using type II censored sample have been derived and compared in term of asymptotic variances and mean square error. The purpose of conducting the empirical study is to study the closeness of MML estimators to ML estimator, and relative efficiency of censored sample to complete sample.