Estimation of P(Y < X) based on Records for Kumaraswamy-Exponential Distribution

Estimation of P(Y < X)

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, the problem of estimation of R = P(Y < X) based on record
values, when X and Y are two independent Kumaraswamy exponential (Kw-E) distributions is considered. The maximum likelihood (ML) estimator of R is obtained. Asymptotic distributions based on ML estimators are also obtained. Monte Carlo simulation is performed to study the behaviour of different estimators.