Work

The One-Parameter Bounded p-Exponential Distribution: Properties, Inference, and Applications

Year: 2026

Type: article

Abstract: We introduce the one-parameter bounded p-exponential distribution on (0, p+1), which includes the uniform model as a special case and converges pointwise to the exponential law as p→∞. Closed-form expressions are derived for the CDF and PDF, the survival function, an explicit increasing-failure-rate hazard function, the quantile function (enabling inversion-based simulation), moments, and entropy, along with a constructive scaled beta or Kumaraswamy representation. We also establish stochastic ordering with respect to p in stop-loss and increasing convex order, formalizing how dispersion varies with the parameter while preserving the mean scale. Inference is discussed under parameter-dependent support, a non-regular setting, and we develop and compare several estimation procedures, including a likelihood-based boundary MLE, a variance-matching method-of-moments estimator, and Bayesian estimation under a gamma prior implemented via numerical quadrature or MCMC. Monte Carlo simulation studies evaluate finite-sample performance and interval behavior, and two real-world applications in survival and reliability analysis illustrate competitive goodness-of-fit relative to standard benchmark models.

Source: Mathematics

DOI: 10.3390/math14061076

Authors: Hassan S. Bakouch, Hugo S. Salinas, Fernando A. Moala, Tassaddaq Hussain, Shaykhah Aldossari, Alanwood Al-Buainain