Comparing Different Estimators for the shape Parameter and the Reliability function of Kumaraswamy Distribution
DOI:
https://doi.org/10.33095/jeas.v25i116.1795Keywords:
Kumaraswamy distribution, the shape parameter, reliability function, maximum likelihood, Bayes method, prior distributions (exponential distribution, chi-squared distribution and Erlang-2 type distribution), the squared error loss function., توزيع Kumaraswamy , معلمة الشكل , دالة المعولية, الإمكان الاعظم ,طريقة بيز , التوزيعات الأولية (التوزيع الاسي , توزيع مربع كاي , توزيع ارلنك),دالة الخسارة التربيعية.Abstract
In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes estimators derived under the squared error loss function. We conduct simulation study, to compare the performance for each estimator, several values of the shape parameter (θ) from Kumaraswamy distribution for data-generating, for different samples sizes (small, medium, and large). Simulation results have shown that the Best method is the Bayes estimation according to the smallest values of mean square errors(MSE) for all samples sizes (n).
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