Generalized unit-exponential distribution and its application to nonparametric Bayesian optimal design

Abdollahi Nanvapisheh, Anita; Jafari, Habib; Khazaei, Soleiman

doi:10.22034/jirss.2026.2022597.1049

Generalized unit-exponential distribution and its application to nonparametric Bayesian optimal design

Articles in Press

Document Type : Original Article

Authors

Anita Abdollahi Nanvapisheh

Habib Jafari

Soleiman Khazaei

1Department of Statistics, Razi University, Kermanshah, Iran.

10.22034/jirss.2026.2022597.1049

Abstract

This study introduces a novel two-parameter distribution, referred to as the Generalized Unit-Exponential (G-UE) distribution, specifically defined on the unit interval. The fundamental mathematical and statistical properties of the proposed distribution are thoroughly investigated. Parameter estimation is carried out using the method of maximum likelihood estimation (MLE). Furthermore, a special case of the proposed distribution obtained when γ = 1 is formulated as a nonlinear regression model. Nonlinear regression models have widespread applications across numerous scientific disciplines, including biostatistics, engineering, and the natural sciences. Achieving an accurate fit for such models is of critical importance, particularly when accounting for potential biases inherent in Bayesian optimal design frameworks. To address these challenges, this study develops a Bayesian optimal design methodology based on the Dirichlet process prior, which represents a fundamental tool in nonparametric Bayesian inference and provides several flexible and analytically tractable representations. The D-optimality criterion is employed in conjunction with the Dirichlet process as a functional prior mechanism to determine the nonparametric Bayesian optimal design.

Keywords

D-optimal design

Bayesian optimal design

Generalized Unit-Exponential model (G-UE)

Dirichlet Process

Stick-Breaking Prior

Nonparametric Bayesian

Subjects

Non-Parametric Statistics

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