Numerical Maximum Likelihood Estimation for the g - and - k Distribution Using Ranked Set Sample

Abstract

The purpose of this paper is to find the estimate of the parameters of g  and  k distribution for ranked set sample by numerically maximizing the likelihood function. The estimates named as numerical maximum likelihood estimate, and corresponding mean square error and relative efficiency compared to simple random sampling are computed using a computer simulation. Ranked set sampling is seen to perform better than the usual simple random sampling method in terms of the efficiency and it is at least as precise as simple random sample. It is found that numerical maximum likelihood estimate using ranked set sample is more efficient than that of simple random sample.