Related papers: Constructions for a bivariate beta distribution
In this paper we have introduced a generalized version of alpha beta skew normal distribution in the same line of Sharafi et al. (2017) and investigated some of its basic properties. The extensions of the proposed distribution have also…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Several distributions are studied, simultaneously in the real, complex, quaternion and octonion cases. Specifically, these are the central, nonsingular matricvariate and matrix multivariate T and beta type II distributions and the joint…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
Properties of the beta functions are investigated. We define the generalized arcsine probability distribution with bounded support. The properties of the beta functions prove some results for this distribution.
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on $\mathbb{R}^2$, to the unit circle. Projected distributions have…
Univariate Weibull distribution is a well-known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters…
We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential…
This short note deals with some applications of the Beta function
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
General classes of bivariate distributions are well studied in literature. Most of these classes are proposed via a copula formulation or extensions of some characterisation properties in the univariate case. In Kundu(2022) we see one such…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…