The Inverse Unit Two-Parameter Mirra Distribution: Properties, Estimation, and Applications

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DOI: https://doi.org/10.28924/2291-8639-24-2026-326
Published: Oct 5, 2026
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Ibrahim Hassan Alkhairy, Jabir Bengalath, Sule Omeiza Bashiru, Hassan Alsuhabi, Mahmoud H. Abu-Moussa, Ramy Aldallal, Eslam Hussam, Ahmed M. Gemeay, The Inverse Unit Two-Parameter Mirra Distribution: Properties, Estimation, and Applications, Int. J. Anal. Appl., 24 (2026), 326.

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Ibrahim Hassan Alkhairy, Jabir Bengalath, Sule Omeiza Bashiru, Hassan Alsuhabi, Mahmoud H. Abu-Moussa, Ramy Aldallal, Eslam Hussam, Ahmed M. Gemeay

Abstract

This paper proposes a new probability distribution called the inverse unit two-parameter Mirra distribution (IUTMD), obtained by applying the inverse transformation scheme to the unit two-parameter Mirra distribution. The proposed model is mathematically simple, preserves the two-parameter structure of the baseline distribution, and provides greater flexibility for modeling positive continuous data. It is defined on the positive real line. Several structural properties of the proposed distribution are derived in closed form, including the survival function, hazard rate function, ordinary moments, incomplete moments, conditional moments, and extropy. The hazard rate function is capable of exhibiting increasing, decreasing, and bathtub shapes, making the proposed model suitable for lifetime and reliability applications. The unknown parameters are estimated using fifteen estimation methods, and a comprehensive Monte Carlo simulation study is conducted to investigate the finite-sample performance of these estimators under different parameter settings and sample sizes. The applicability of the proposed model is illustrated using two real datasets involving precipitation measurements and the lifetimes of electronic components. The performance of the proposed distribution is compared with several existing competing distributions using standard goodness-of-fit measures and information criteria. The results show that the proposed distribution provides a better fit to the datasets considered and offers a flexible and useful model for positive continuous data.

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