Exploring Beta-Like Distributions

TL;DR

This paper introduces a family of Beta-like distributions that incorporate additional data such as predictor variables and failure times, extending the classical Beta distribution for more complex probabilistic modeling.

Contribution

The paper derives a new family of Beta-like distributions that integrate predictor variables and temporal data, broadening the applicability of Beta distributions.

Findings

Derived a family of Beta-like distributions incorporating predictor variables.

Extended Beta distribution to include time-to-failure data.

Provides a framework for more flexible probabilistic modeling.

Abstract

The most well known probability distribution of probabilities is the Beta distribution. If we have observed $r$ `successes', each having a probability $\theta$, and $n-r$ `failures', each having a probability $1-\theta$. In this paper we will derive a whole family of Beta-like distributions, which take as their data not only the number of successes and failures, but also values on predictor variables and time to failure or time without failure.