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Related papers: Constructions for a bivariate beta distribution

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For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…

Statistics Theory · Mathematics 2020-09-09 Aziz LMoudden , Éric Marchand

Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…

Methodology · Statistics 2023-05-02 Mayad Al-Saidi , Alexey Kuznetsov , Mikhail Nediak

This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.

Classical Analysis and ODEs · Mathematics 2013-04-25 Charles F. Dunkl

The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders…

Methodology · Statistics 2012-04-30 Artur J. Lemonte , Guillermo Martínez-Florez , Germán Moreno-Arenas

In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…

Statistics Theory · Mathematics 2019-05-31 Anwar Hassan , Ishfaq Shah Ahmad , Peer Bilal Ahmad

This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and…

Probability · Mathematics 2026-01-14 Jakub Gismatullin , Patrick Tardivel

Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…

Computation · Statistics 2015-08-21 Roberto C. Crackel , James M. Flegal

There exist several endeavors proposing a new family of extended distributions using the beta-generating technique. This is a well-known mechanism in developing flexible distributions, by embedding the cumulative distribution function (cdf)…

Statistics Theory · Mathematics 2019-12-17 M. Arashi , A. Bekker , D. de Waal , S. Makgai

The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some…

Statistics Theory · Mathematics 2020-07-27 Roberto Vila , Jeremias Leão , Helton Saulo , Mirza Nabeed , Manoel Santos-Neto

Beta regression is often used to model the relationship between a dependent variable that assumes values on the open interval (0,1) and a set of predictor variables. An important challenge in beta regression is to find residuals whose…

Methodology · Statistics 2017-04-11 Gustavo H. A. Pereira

The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…

Classical Analysis and ODEs · Mathematics 2020-01-14 A. Gil , J. Segura , N. M. Temme

Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…

Methodology · Statistics 2022-03-08 Emily A. Cooper , Hany Farid

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

Probability · Mathematics 2026-05-15 Palaniappan Vellaisamy , Puja Pandey

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

Methodology · Statistics 2021-03-04 Vincenzo Gioia , Euloge Clovis Kenne Pagui

Probability distribution theory helps in studying the impact of various dimensions in life while the Mittag-Leffler function and bicomplex are used in electromagnetism, quantum mechanics, and signal theory. Considering the importance of…

Probability · Mathematics 2024-11-22 Dharmendra Kumar Singh , Chinmay Sharma

The binomial and Poisson distributions have interesting relationships with the beta and gamma distributions, respectively, which involve their cumulative distribution functions and the use of conjugate priors in Bayesian statistics. We…

Statistics Theory · Mathematics 2016-10-25 Peter Peskun

The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisation of when one Beta distribution is smaller than another…

Probability · Mathematics 2021-01-01 Idir Arab , Paulo Eduardo Oliveira , Tilo Wiklund

A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…

Statistics Theory · Mathematics 2015-07-28 Haim Shore

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

Probability · Mathematics 2018-06-22 Shane Barratt

Statistical inference in high-dimensional settings is challenging when standard unregularized methods are employed. In this work, we focus on the case of multiple correlated proportions for which we develop a Bayesian inference framework.…

Methodology · Statistics 2025-06-23 Max Westphal