The Kernel Inference on the Rayleigh Distribution based on the Complete Sample

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Abstract In this paper, we suggest a procedure based on the non-parametric kernel function as an alternative and reliable technique 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 Bayesian estimation based on both non-informative and informative conjugate priors, which indicates the robustness of the proposed method over the Bayesian approach. To clarify that, via Monte Carlo simulations, we derived the point and interval estimates of the parameter and the reliability of the Rayleigh distribution based on the two approaches. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.

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