One parameter stochastic distribution of ratio for cross-disciplinary applications: system reliability, healthcare, and energy consumption

Muhammad Ilyas and Muhammad Mohsin

Journal of Applied Statistics, 2026, vol. 53, issue 4, 590-613

Abstract: Statistical modeling of real-life phenomena analyzes their behavior and patterns by quantifying the inherent uncertainty and describes the possible outcomes which help to make proactive strategies attaining optimum results. This paper introduces a one parameter stochastic distribution of ratio derived from the bivariate conditional Weibull distribution to model the data sets from diverse fields such as system reliability, healthcare and energy consumption. Some important features and statistical properties of the proposed distribution are presented. A simulation study is conducted by using the acceptance–rejection method to evaluate the stability of the model parameter based on its average estimated values, standard errors, and biases. The parameter of the proposed distribution is estimated by using maximum likelihood and Bayesian methods. The proposed model and some extant models are employed on the ratio of downtimes to the total times, case fatality rate and proportion of cooling energy. The comparison of the results establishes the competency of the proposed model. The estimated quantiles for the three different data sets provide insights about the potential range of system reliability in terms of downtime to the total time, case fatality rate and energy consumption for cooling the buildings.

Date: 2026
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DOI: 10.1080/02664763.2025.2525884

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