We propose inference of the stress strength parameter, R=P(Y<X), when X and Y are independent generalized exponential-Poisson random variables. The problem of classical and Bayesian estimation of R is discussed. The Metropolis-Hastings algorithm is used to approximate the posteriors of R. Bayesian informative priors are considered under symmetric and asymmetric loss functions. Asymptotic confidence intervals for R are proposed. Monte Carlo simulations are performed to compare the proposed methods. At the end, a real dataset is analyzed for illustrative purposes.
Here, we consider estimation of the pdf and the CDF of the Weibull distribution. The following estimators are considered: uniformly minimum variance unbiased, maximum likelihood (ML), percentile, least squares and weight least squares. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others.
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