A multi-parametric unit distribution via Bernstein polynomials

This study develops the method of constructing a multi-parametric distribution on the unit interval using Bernstein polynomials and investigates its key statistical properties. The performance of the proposed distribution’s parameter estimators was evaluated by Monte Carlo simulation under both maximum-likelihood (MLE) and minimum-distance frameworks, with the MLE approach generally yielding lower estimation error. A real data example illustrates the advantages of the construction method. The results reveal that the Bernstein distribution provides superior goodness-of-fit to the dataset compared with competing models.