Power Lindley-Logarithmic Distribution And Parameter Estimation

Statistics has attracted more and more attentions and been applied in many areas,and it also derives many subdisciplines,such as survival analysis,regression analysis,reliability statistics and hypothesis testing.For all subdisciplines,the research on sta-tistical distribution is indispensable.As one of the important compositions of statistical distribution,lifetime distribution plays an important role in the study field of science and technology.With the development of lifetime distribution theory,people have pro-posed a variety of methods to generate new lifetime distributions,which facilitate the study of lifetime data.In this article,by compounding the Power Lindley distribution and the Logarithmic distribution,we generate a three parameter new lifetime distri-bution with various forms of hazard rate,and study the statistical properties and the parameter estimation problem of the distribution.Chapter one introduces the research background and current situation,and al-so briefly introduces the Power Lindley distribution and the Logarithmic distribution;Chapter two constructs the Power Lindley-Logarithmic distribution,and discusses its statistic properties such as the density function,the quantile function,entropy,mo-ment,hazard rate function,mean residual life and the asymptotic distribution of the minimum value;Chapter three gives the maximum likelihood estimation(MLE)of this distribution,and proves the consistency and asymptotic normality of the MLE under the large sam-ple.The EM algorithmic is used to derive the MLE;Chapter four simulates the point estimation and the interval estimation of the M-LE using Monte Carlo method,then inspects the effect of estimation and the coverage of the asymptotic confidence interval under different sample sizes.