Related papers: Exploring Beta-Like Distributions
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
A new generalization of the family of Poisson-G is called beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived and seen as…
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…
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…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…
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 article analyzes the problem of estimating the time until an event occurs, also known as survival modeling. We observe through substantial experiments on large real-world datasets and use-cases that populations are largely…
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.
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…
We study with some details a lifetime model of the class of beta generalized models, called the beta inverse Rayleigh distribution, which is a special case of the Beta Fr\'echet distribution. We provide a better foundation for some…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
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…
In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful…
We consider the zeta distributions which are discrete power law distributions that can be interpreted as the counterparts of the continuous Pareto distributions with unit scale. The family of zeta distributions forms a discrete exponential…
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…