On a new test of fit to the beta distribution

TL;DR

This paper introduces a new goodness-of-fit test for beta distributions using an $L^2$-type approach based on a conditional moment characterization, with demonstrated superior performance over classical tests.

Contribution

It develops a novel $L^2$-based test for beta distribution fit, including its asymptotic distribution, bootstrap calibration, and validation through simulations and real data.

Findings

The test outperforms classical goodness-of-fit tests in simulations.

The asymptotic null distribution depends on parameters, requiring bootstrap.

Application to air humidity data demonstrates practical utility.

Abstract

We propose a new $L^2$-type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.