Power Lindley-Logarithmic分布及其参数估计

Power Lindley-Logarithmic Distribution and Parameter Estimation

将Power Lindley分布和Logarithmic分布“混合”得到一个危险率形式多样的新型寿命分布Power Lindley-Logarith⁃mic(PPL)分布,研究了该分布的矩、分位数、危险率函数、顺序统计量的极限分布和参数的极大似然估计(maximum likelihood estimation,MLE),验证了极大似然估计的相合性和渐近正态性,应用EM(expectation-maximization)算法求参数的极大似然估计,并进行了Monte Carlo模拟.模拟实验表明,EM算法得到的参数的极大似然估计很好地反映了参数的真值,且PPL分布参数的极大似然估计具有良好的渐近正态性.

This paper proposes a new lifetime distribution named Power Lindley-Logarithmic distribution(PLL)by compounding the Power Lindley distribution and the Logarithmic distribution.In the paper,its moment,quantile,hazard rate function,limiting distribution of the order statistics and the MLE(maximum likelihood estimation)of the parameters are discussed,the consistency and asymptotic normality of the MLE are verified,and EM(expectation-maximization)algorithm is used to get the MLE.In the end,the paper carries out Monte Carlo simulation which indicates that the MLE obtained by EM algorithm perfectly reflects the true value of the parameters,and the parameters’MLE of the PPL distribution have good asymptotic normality.