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In this paper, we consider a location-scale family arising out of Absolutely Continuous Trivariate Exponential (ACTVE) distribution with equal marginal due to Weier and Basu. The distribution of the complete sufficient statistic is obtained by first proving a result on spacings similar to the results of Sukhatme for univariate exponential distribution. The UMRUE with respect to any loss function convex in the second argument of the location – scale parameter is obtained. Following the simultaneous equivariant estimation approach of Edwin Prabhakaran and Chandrasekar, we derive the minimum risk equivariant estimator of the location -scale parameter. Further the equivariant estimation of percentiles of the population is also discussed. UMP tests for ACTVE location-scale family are also derived.

Exact inference for the parameters of absolutely continuous trivariate exponential location–scale model