This article considers the estimation of R = P(Y < X) when X and Y are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate R on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes.

In this article, we consider the estimation of P[Y < X], when Y and X are two independent scaled Burr Type X distribution having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator, and approximate Bayes estimators of P[Y < X] are discussed. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations. One data set has been analyzed for illustrative purposes.

In this paper we consider the generalized exponential distribution with known shape parameter Θ. We first derive the exact forms of means, variances and covariances of order statistics. We use these expressions in obtaining the necessary coefficients for the best linear unbiased estimators of the location and scale parameters for Θ=0.5(0.5)5.0 and for sample sizes up to ten. The variances and covariances of these estimators are also given.