L-Moments and TL - Moments Estimation and Recurrence Relations for Higher Moments of Order Statistics from Lindley Distribution

Order Statistics from Lindley Distribution

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

In this paper, we have obtained L-moments and TL-moments of Lindley distribution and used them to find the L-moments and TL-moments estimator of the parameter of the Lindley distribution. Also we have obtained the recurrence relations for higher moments of order statistics arising from doubly truncated Lindely distribution which enable one to obtain all the single, double (product) and higher moments of any order of all order statistics for any sample size in a simple recursive manner. Also, the corresponding recurrence relations for untruncated Lindley distribution have been obtained as special cases.