Abstract

In this paper some of the important statistical properties and applications of new X-Lindley distribution which were not studied earlier has been studied. The statistical properties based on moments including coefficient of variation, coefficient of Skewness, coefficient of kurtosis and index of dispersion have been derived and their behaviors examined graphically. Moment generating function, characteristics function, and conditional mean and conditional variance has been discussed derived. The reliability properties including survival function, hazard function, reverse hazard function, mean residual life function, stochastic ordering and stress-strength reliability have also been discussed along with deviation from mean and median, Bonferroni and Lorenz curve and their indices. The sequential probability ratio test and approximation for the average sample number have been discussed. The parameters of the distribution are estimated using method of moments, maximum likelihood estimation, maximum product spacing estimation, least square estimation, weighted least square estimation, Crammer-Von Mises estimation and Anderson-Darling estimation. A simulation study is carried out using acceptance-rejection method of simulation to know the consistency of the estimate values of the parameter. A goodness of fit measures has been shown on two real life datasets from the engineering field and compared with almost all one parameter lifetime distributions introduced in statistics literature. 

Keywords

hazard function, mean residual life function, estimation, simulation study, applications