# Some methods to approximate and estimate the reliability function of inverse Rayleigh distribution

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## Keywords:

Inverse Rayleigh, Maximum-likelihood, NLINEX loos function, Chi-squared, Bernstein polynomials## Abstract

In this paper, three methods to find the reliability function for inverse Rayleigh distribution are introduced. The first one, the reliability function is expanded using Bernstein polynomials to find the approximate solution of it. The second one, the maximum likelihood is applied to estimate the scale parameter to find the reliability function. The third one, the Bayes estimator is developed under the NLINEX loss function to find the reliability function with the least loss where this estimator is derived using chi-squared informative prior distribution. The results of all methods depending on the integrated mean squared error (IMSE) are compared to find which of these methods is best by using the simulation technique. Finally, to determine theoretical results MATLAB 2015 is used**.**

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