A Bivariate Beta Distribution with Arbitrary Beta Marginals and its Generalization to a Correlated Dirichlet Distribution

04/16/2021
by   Susanne Trick, et al.
0

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of the distribution can be fit to data using moment matching. Previous work used an approximate and sometimes inaccurate method to compute the covariance. Here, we derive all product moments and the exact covariance, which can easily be computed numerically. The bivariate case can be generalized to a multivariate distribution with arbitrary beta-distributed marginals. Furthermore, we generalize the distribution from two marginal beta to two marginal Dirichlet distributions. The resulting correlated Dirichlet distribution makes it possible to model two correlated Dirichlet-distributed random vectors.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/16/2019

Developing multivariate distributions using Dirichlet generator

There exist several endeavors proposing a new family of extended distrib...
research
10/31/2019

Simultaneous Inference for Multiple Proportions: A Multivariate Beta-Binomial Model

In this work, the construction of an m-dimensional Beta distribution fro...
research
06/03/2021

A Normative Model of Classifier Fusion

Combining the outputs of multiple classifiers or experts into a single p...
research
03/02/2023

Bivariate beta distribution: parameter inference and diagnostics

Correlated proportions appear in many real-world applications and presen...
research
05/29/2023

A flexible Clayton-like spatial copula with application to bounded support data

The Gaussian copula is a powerful tool that has been widely used to mode...
research
10/31/2016

Bayesian Adaptive Data Analysis Guarantees from Subgaussianity

The new field of adaptive data analysis seeks to provide algorithms and ...
research
10/12/2018

Mean field voter model on networks and multi-variate beta distribution

The regional characteristics of elections show a strong spatial correlat...

Please sign up or login with your details

Forgot password? Click here to reset