ESTIMATION OF ORDERED PARAMETERS FOR SOME DISTRIBUTIONS

Abstract

Let nl, 112,...,nk be k populations with associated probability distribution being characterized by parameters 01,...,0k respectively. The problem of estimating the order restricted parameters when ordering is known a- priori is of considerable interest. These kinds of problems arise in various agricultural, biotechnology, industrial, engineering and economic experiments. For example, if tv< t2...< tk, then it is natural to assume el< 02 < ...<0k. Or in planning the requirement of certain items depend upon income of people. If the requirement is directly proportional to income of people, It is reasonable to assume the average requirement (say 0i) in order to income group of the people. In present study we concern mainly estimating ordered parameters in two populations i.e. (k= 2). The problem of estimation of ordered scale parameters of some distributions has been considered. First the problem of estimation of the ordered scale parameters of „ two Pareto populations has been considered. Two maximum likelihood estimators of ordered scale parameters are obtained, one B-Z MLE and another D-MLE. The nonexistence of unbiased estimator for ordered scale parameters has been shown. An admissible class of estimators in scalar multiple class has been found using Brewster- Zidek technique. Thus concluding that the above two maximum likelihood estimators obtained are inadmissible. The bias and risks of these estimators are calculated. The minimax estimators with respect to absolute bias risk criterion are obtained for both ordered scale parameters.