Bayes estimation of a distribution function using ranked set samples

Aranked set sample (RSS), if not balanced, is simply a sample of independen t order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a genera l RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inferen ce. In such cases, Bayes estimators should be considered for improved estim ation. Bayes estimation (using the squared error loss function) of the unkn own distribution function F is investigated with such samples. Additionally , the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based on the EM Algorithm is used to produce the GMLE of F . For the case of squared error loss, simple solutions are uncommon, and a procedure to find the solution to the Bayes estimate using the Gibbs sample r is illustrated. The methods are illustrated with data from the Natural En vironmental Research Council of Great Britain (1975), representing water di scharge of floods on the Nidd River in Yorkshire, England.