Cumulative Residual Extropy properties of Ranked Set Sample for Cambanis Type Bivariate Distributions

Cumulative Residual Extropy Properties of Ranked Set Sample

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 consider the  cumulative residual extropy (CREX) of concomitant of order statistic and its properties, when samples are taken from Cambanis family of distributions. By using the expression for CREX of concomitants of order statistics, the CREX of the RSS observations is obtained, when the study variate $ Y $ is difficult to measure but an auxiliary variable $ X $ is used to rank the units in each set, under the assumption that $ (X,Y) $ follows Cambanis type bivariate distributions.