Modeling Proportional Data in Public Health and Drone Detection: Frequentist and Bayesian Inference for the Novel Sine Unit Distribution

Rasha Alyousef¹, Amal S. Hassan², Omar A. Saudi³, Ohud A. Alqasem⁴, Mohammed Elgarhy^5,6,*
1 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
2 Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza, Egypt
3 Department of Basic Sciences, Higher Institute of Management Sciences (HIMS), Katameya, New Cairo, Egypt
4 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
5 Faculty of Computers and Information Systems, Egyptian Chinese University, Nasr City, Egypt
6 Department of Computer Engineering, Biruni University, Istanbul, Turkey
* Corresponding Author: Mohammed Elgarhy. Email: Mohammed.Elgarhy@ecu.edu.eg
(This article belongs to the Special Issue: Computer Modeling in Statistics)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.085404

Received 11 May 2026; Accepted 17 August 2026; Published online 28 August 2026

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Abstract

It is of utmost importance to develop probability models that can cope with asymmetry for an effective analysis of asymmetrical real-world data. In this context, the current paper proposes a new unit asymmetric probability distribution for the interval (0, 1). The sine unit inverse exponentiated Pareto probability distribution is developed through the application of the sine-G family of transformations to the unit inverse exponentiated Pareto probability distribution. The inherent flexibility of the proposed distribution makes it have high potential for practical applications in the analysis of asymmetry in real-life data sets. Explicit formulas for some important statistical properties are obtained; these include the moment generating function, ordinary moments, quantile function, incomplete moments, stress-strength reliability and two entropy measures. In particular, issues related to parameter estimation, using maximum likelihood and Bayesian methods with symmetric and asymmetric loss, are discussed. To overcome the analytically intractable integration in Bayesian estimation under symmetric and asymmetric losses, the Metropolis–Hastings algorithm with independent gamma priors is applied within a Markov Chain Monte Carlo scheme. All computations and Monte Carlo performance evaluations are executed using the R programming language along with specific libraries (‘maxLik’ and ‘MCMCpack’). From a numerical study, we observe that, as anticipated, the increase in sample size improves precision, and Bayesian estimators outperform their maximum likelihood competitors under different scenarios because of their lower mean squared error values. The usefulness of the distribution in practical situations is highlighted by application in two different situations; firstly, in modeling the mortality rate of COVID-19 and secondly, in evaluating the efficiency of detecting unmanned aerial systems. Seven other competitive unit distributions are compared using eight criteria of goodness-of-fit. This study presents the utility of the new model in being an effective means of dealing with uncertainties while providing reliable estimation of parameters when such tools are required in epidemiological and defense security studies.