Statistical Analysis Of The Lindley Distribution

Lindley distribution is one of distributions which can be used to analy life data,it was first proposed by Lindley in 1958 in the literature[1].It shows that the distribution has a good adaptability and flexibility,and plays an important role on the reliability of stress-strength model.Therefore,it is necessary to study the statistical properties of the distribution.In this paper,we first introduce the distribution function of Lindley distribution,give the function and its image of probability density,coefficient of variation,skewness,kurtosis,failure rate and so on,and illustrate the main digital features of the distribution.Then,the point estimation and interval estimation of the parameters are discussed in the case of the whole sample,the advantages and disadvantages of the two methods of interval estimation are compared by simulation study.The applicability of the method is illustrated by examples.Next,this paper focuses on the parameter estimation of Lindley distribution in the case of censoring samples.We discuss the point estimation and the interval estimation of the parameter under the type II censoring samples.Monte-Carlo simulation is used to compare the maximum likelihood estimation and the inverse moment estimation,which shows the estimation of the inverse moment is of good accuracy.The simulation results show that the interval estimation method can meet the reliability requirements.Then,by fitting testing of several examples,we may see that the Lindley distribution has better adaptability than exponential distribution.Next,we discuss the interval estimation of Lindley distribution in the case of type I censoring samples.The stochastic simulation shows that the method is feasible in terms of the confidence level.The feasibility of the method is also illustrated by real examples.Then,the point estimation and interval estimation of Lindley distribution under the left truncation samples are studied.The maximum likelihood estimation and inverse moment estimation of the parameter are given,and the two methods are compared by stochastic simulation,which shows that the maximum likelihood estimation has better accuracy.The Monte-Carlo simulation is also used to test the interval estimation,it shows that the method can meet the reliability requirements,and we illustrate the feasibility and practicability of this method through real examples.Finally,we find that if X obeys Lindley distribution with parameter ?,let Z =1 X,when Z obeys the inverse Lindley distribution with parameter ?.So the Lindley distribution under the left truncation samples can be regarded as the inverse Lindley distribution in the type II censoring sample,the method of point estimation and interval estimation can also be used to discuss the parameter estimation of the inverse Lindley distribution based on censored samples.