Natural exponential family

About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Abstract: Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios Despite being well-studied on an abstract level, the number of known parametric families is small Furthermore, for most families only implicit stochastic representations are known The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Harris Extended Exponential Distribution

Abstract: In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function and hazard function of the Harris extended exponential distribution. The case of reversed hazard function was excluded because of its complexity. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions, functions and can serve an alternative to estimation and approximation.

A new bivariate distribution in natural exponential family

Abstract: We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).

The Exponentiated G Poisson Model

Abstract: We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general exponentiated G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability, and Shannon entropy are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform an application to a real data set to show the potentiality of the proposed family.