Marshall-Olkin Extended Rayleigh Distribution and Applications

Marshall-Olkin Extended Rayleigh 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 a new lifetime distribution as a two parameter generalization of Rayleigh distribution namely Marshall Olkin Extended Rayleigh distribution is introduced and studied. The statistical properties such as quantile function, moments, compounding properties, R´enyi entropy and stochastic ordering etc. are explored. The distribution of order statistics and its asymptotic distribution are derived. As an application of the distribution to the record value theory we evaluate the first and second single moment of nth upper record value. The method of maximum likelihood is used to estimate the unknown parameters. The results are validated using real data sets.