An alternative to continuous univariate distributions supported on a bounded interval: The BMT distribution

TL;DR

The paper introduces the BMT distribution, a new unimodal distribution inspired by Bezier curves, offering a flexible alternative for modeling bounded data, with applications demonstrated on real datasets.

Contribution

It presents the formulation, properties, and estimation methods of the BMT distribution, a novel distribution derived from geometric design principles.

Findings

Effective parameter estimation via maximum likelihood and maximum product of spacing.

Demonstrated flexibility and usefulness on three real data sets.

Potential to model data beyond beta distribution scope.

Abstract

In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer aid geometric design, specifically from Bezier curves. First, we review general properties of a distribution given by parametric equations and extend the definition of a Bezier distribution. Then, after proposing the BMT cumulative distribution function, we derive its probability density function and a closed-form expression for quantile function, median, interquartile range, mode, and moments. The domain change from [0,1] to [c,d] is mentioned. Estimation of parameters is approached by the methods of maximum likelihood and maximum product of spacing. We test the numerical estimation procedures using some simulated data. Usefulness and flexibility of the new distribution are illustrated in three real data sets. The BMT distribution has a significant potential to estimate domain parameters and to model data outside the scope of the beta or similar distributions.