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A comparison of Bayesian and non-Bayesian Methods for Estimation of Reliability function and Hazard function for Lomax Distribution with two parameters | ||
| Baghdad College of Economic sciences University | ||
| Article 1, Volume 0, Issue 43, 2018, Pages 445-456 | ||
| Author | ||
| Dr.Safaa Ali Naser | ||
| Abstract | ||
| Lomax distribution also called the pareto type II distribution is a heavy-tail probability often used in business and life testing, Reliability, with extended application in economic science and actuarial modeling , queuing problems , and biological science. Panahi and Asadi (2011) studied estimation of the stress-strength parameter R=P(YY) when X,Y are independent random variables , and introduce a new family of distribution referred to as the double Lomax distribution and derive the p.d.f and the expression for the reliability R for the double Lomax distribution truncated below zero. David ,Hui ,and Ryan (2011) analyzed the second-order bias of the maximum likelihood estimators for Lomax (Pareto II) distribution for finite sample size and show that this bias is positive . Asghar zadeh and Valiollahi (2011) derived explicit estimator for Lomax distribution by approximating the likelihood function . Morteza , Farhad and Manoochehr (2012) they use the Bayesian estimators for Lomax distribution obtained thought conjugate prior for the shape and scale parameters under generalized order statistics. In this study we explore and compare the performance of the maximum likelihood and least square and moment estimates with the Bayesian of Reliability and Hazard function for the two parameter Lomax distribution. The probability density function of two parameter Lomax distribution becomes : Where α is shape parameter , λ is the scatter parameter of the distribution. The reliability function is given by : ………..(2) And the Hazard function become : …… (3) The rest of the paper is arranged as follows . The methods , Maximum likelihood estimator, least square estimator , Bayes estimator , estimator of moment method . In results , Simulation study is discussed and the results are presented and followed by conclusion. | ||
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