On Moments of Order Statistics from Extended Normal 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 introduced a two-parameter distribution, “Extended Normal Distribution”, observed as a bimodal symmetric distribution, of which Normal distribution is a particular case. Its moments, inverse moments, maximum likelihood estimators and other statistical measures have been discussed. For few particular values of unknown parameters, we have obtained the exact moments and the recurrence relation for moments of order statistics arising from Extended Normal Distribution.