The Maximum Likelihood Estimates Of Parameters In Generalized Bernoulli Distribution By The Excellent Ranked Set Sampling

Much of the RSS literatures refer to random variables of the one parameter type, and gain abundant research results. Nevertheless, some multiple parameter conditions are also need to study, such as the generalized bernoulli distribution population. In this article, we estimate the parameters of the generalized bernoulli distribution which we are interested in under maximum likelihood estimation (MLE), and find the optimal design under unbalanced ranked-set sampling (URSS). We know that multiple parameter MLE has asymptotic normal distributions, so the optimal design which we need to find is that optimizing the asymptotic covariance matrix. In this article, we render the standard which minimizing the asymptotic covariance matrix as our scheme, and we call this scheme as D-optimal scheme. Here, we suppose the ranking is perfect, and provide specific actionable process with regard to the disperse population. It has been shown that we can find the optimal design which contains no more than three order statistics under this D-optimal scheme, and population parameters can be estimated more precisely using optimal design RSS as opposed to BRSS under MLE when the knowledge of the underlying distribution is available.