A numerical comparison between the approximation and the estimation of the reversed hazard rate function for the inverted Kumaraswamy distribution

What is it about?

Abstract. The unknown shape parameter of the inverse Kumaraswamy distribution and some other life-time properties such as the reversed hazard rate function (RHRF) deriving based on complete data, and imposed another shape parameter is known were introduced. Three methods for estimating the reversed hazard rate function were used. Maximum likelihood estimation (MLE) method was used for the non-Bayesian estimator, as well as using the Bayesian estimators with two informative priors (Gamma and Exponential) under symmetric (squared error loss (SEL) function) and asymmetric (entropy loss (EL) function) to estimate the reversed hazard rate function, which was approximated using a numerical method (Boubaker polynomials (BbP) method). The different estimators were compared experimentally by adopting the Monte Carlo simulation study, also comparing the estimators and the approximation for the reversed hazard rate function depending on the integrated mean squared error (IMSE). The program (MATLAB 2015) was used to obtain the numerical calculations.

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Why is it important?

In this paper, the most fundamental conclusions are summed up by all results the better priors for the Bayes estimator based on the squared error loss function are exponential prior distribution and the better loss function is a squared error. The values of integrated mean squared error related to non-Bayes are less than Bayes estimates and approximated values are less than non-Bayes and Bayes estimates for all sample sizes. Also, through the results, it was found that the numerical method (Boubaker polynomials method) is more efficient than the estimation methods (non-Bayes and Bayes) in estimating the function of the reversed hazard rate for inverse Kumaraswamy distribution.

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