Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both Rényi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that Rényi and Tsallis entropies c...

normal 0 false false false en-us x-none ar-sa microsoftinternetexplorer4 background: urban living and transition of illnesses, today has led hygienic centers for dedicating services to serious challenge management of an outpatient center is very difficult. worse is that the patient advice and service time is much less than waiting time. many people to avoid long waiting go to private treatment ...

We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...

We characterize, up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positivity condit...

Standardized Runoff Index (SRI), as one of the well-known hydrological drought indices, may contain uncertainties caused by employment distribution function, time scale, and record length statistical data. In this study, uncertainty in SRI estimation monthly discharge data 30- 49-year lengths from Minab Dam watershed, south Iran, was investigated. Four probability functions (Gamma, Weibull, Log...

In this paper, we study a mixed cooperative communication system consisting of power line (PLC) and free-space optical (FSO) links, where the PLC link suffers from log-normal fading is affected by both impulsive background noises. Meanwhile, FSO undergoes Gamma-Gamma with atmospheric turbulence pointing errors. More specifically, present closed-form expressions for probability density function ...

In mixtures-of-experts (ME) models, "experts" of generalized linear models are combined, according to a set of local weights called the "gating function". The invariant transformations of the ME probability density functions include the permutations of the expert labels and the translations of the parameters in the gating functions. Under certain conditions, we show that the ME systems are iden...

Abstract— Aim: The aim of this study is to develop a public web-based theoretical probability distributions software (KODY) that can calculate probabilities for discrete and continuous distributions.
 
 Materials Methods: Discrete Uniform, Bernoulli, Binomial, Multinomial, Poisson, Geometric, Negative Hypergeometric Zeta (Zipf) from the are explained. Among distributions, Continuous B...