The Bayesian Estimation For Exponentiated-weibull Distribution And Its Simulation

Among many of the life distribution types, Exponentiated Weibull distribution has alot of good properties and is widely used. Compared with the Exponential distribution andWeibull distribution, it can fit more type of data, include the bath-tub data, and the data ofsingle peak failure rate. Thus, many scholars had studied the properties of its parameter、Failure-rate、Reliability,but most of them adopt the classical statistical method, or selectthe simpler prior distribution to study the basic properties of Bayesian estimate.This paper is on the basis of previous studies, use the basic principle of Bayesianmethod. Introduce the MLE and Bayesian estimation of Exponentiated Weibul-l distribution,s parameters α and θ、Reliability R(t) and Failure-rate H(t) under differentloss function.The first chapter presents the concept of Exponentiated Weibull distributionand its application situation, also the timing truncated test is introduced in it,and flowingit,we specify the frame structure of this paper.As the prepare knowledge,the second chap-ter introduces the basic theory of bayesian estimation、square loss function、LINEX lossfunction and the bayes estimation under the two loss functions.In the third chapter,we firsttalk about the MLEs of the two parameters α and θ，Failure-rate H(t)、Reliability R(t)，then the bayesian estimations of theirs are gained under the square loss function and LINEXloss function with the parameter α known. Then we give numerical simulation of theseestimations to draw some conclusions. The fourth chapter based on the Lindely approxima-tion theorem, the Bayesian estimations of the two parameters α and θ, Failure-rate H(t)、Reliability R(t) are given when the two parameters are unknown.The numerical simulationof estimations and the brief conclusion analysis are also given.At last,we further prospect the conclusion of this paper.