Unit one parameter polynomial exponential distribution

Molay Kumar Ruidas

doi:10.1080/02331888.2025.2574291

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Unit one parameter polynomial exponential distribution

2025-10-01

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Molay Kumar Ruidas

Mriganka Mouli Choudhury

Sudhansu S. Maiti *

DOI：10.1080/02331888.2025.2574291

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Abstract

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In this study, we propose the Unit One Parameter Polynomial Exponential (unit-OPPE) distribution and look into some of its mathematical properties while taking into account the transformation $ X = \frac {Z}{1+Z} $ X=Z1+Z, where the random variable Z follows OPPE distribution with parameter theta. Distributional properties like moments, mode, characterization using conditional moments, reliability measures, and stochastic ordering are addressed. Maximum likelihood (ML) and uniform minimum variance unbiased (UMVU) estimation methods are used to estimate the model parameter. The same are also used to estimate the probability density function, cumulative density function, and reliability function. Some other estimation methods like Least Square estimation (LSE), Weighted Least Square estimation (WLSE), Anderson-Darling estimation (ADE), Cramer-Von-Mises estimation (CME), Maximum Product of Spacings estimation (MPSE) of the parameter are also discussed. The bias and mean square error (MSE) of the parameter estimates are investigated using Monte Carlo simulation. Finally, four real-world applications demonstrate how our unit-OPPE model fits better than the beta, unit-Lindley, unit-Zeghdoudi, unit-Half Normal, Kumaraswamy, unit-Gompertz, and unit-Xgamma models.

Keywords:

Unit-Lindley distribution

incomplete moments

reliability measures

maximum likelihood estimator

uniformly minimum variance unbiased estimator