Estimation of the Exponential Distribution Parameter and Reliability Based on the Kernel and Bayes Approaches

Abstract

Abstract We suggest herein a procedure for estimating the distribution parameters and reliability based on the non-parametric kernel density function. This technique has been utilized as an alternative and reliable approach for estimation in life-testing models directly from the data without any prior assumptions about the underlying distribution parameters. The efficiency of this technique has been studied compared to the Bayesian approach for estimating the parameter and reliability of the exponential distribution via Monte Carlo simulations. The simulation results indicated the robustness of the proposed method over the Bayesian approach based on the informative and informative conjugate priors. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.