Axioms (Sep 2022)

A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

  • Faiza A. Althubyani,
  • Ahmed M. T. Abd El-Bar,
  • Mohamad A. Fawzy,
  • Ahmed M. Gemeay

DOI
https://doi.org/10.3390/axioms11100504
Journal volume & issue
Vol. 11, no. 10
p. 504

Abstract

Read online

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.

Keywords