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 Size-Biased Double Weighted Exponential Distribution (SDWED)

Abstract: This paper introduces a new distribution based on the exponential distribution, known as Size-biased Double Weighted Exponential Distribution (SDWED) Some characteristics of the new distribution are obtained Plots for the cumulative distribution function, pdf and hazard function, tables with values of skewness and kurtosis are provided As a motivation, the statistical application of the results to a problem of ball bearing data has been provided It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distribution It is found that our newly proposed distribution fits better than size-biased Rayleigh and Maxwell distributions and many other distributions Since many researchers have studied the procedure of the weighted distributions in the estates of forest, biomedicine and biostatistics etc, we hope in numerous fields of theoretical and applied sciences, the findings of this paper will be useful for the practitioners

Bounds on Tail Probabilities in Exponential families

Abstract: In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial distributions, the negative binomial distributions and the inverse Gaussian distributions. All these exponential families have simple variance functions and the variance functions play an important role in the exposition. All the inequalities presented in this paper are formulated in terms of the signed log-likelihood. The inequalities are of a qualitative nature in that they can be formulated either in terms of stochastic domination or in terms of an intersection property that states that a certain discrete distribution is very close to a certain continuous distribution.

Discrete analytic functions of exponential growth

Abstract: Analogues of classical representation formulas for entire functions of exponential type are proved in the class of discrete analytic functions.