Halim Zeghdoudi

This study introduces a novel one-parameter probability distribution called the QGamma distribution (QGaD), constructed through a specific mixture of the exponential and Chris–Jerry distributions. The mathematical properties of the QGaD are thoroughly investigated, including its probability density function, cumulative distribution function, moments, variance, mean residual life function, order statistics, and hazard rate function. Fifteen classical estimation methods are employed to estimate its parameter, with their performance evaluated through a Monte Carlo simulation. The flexibility and modeling capability of the proposed distribution are assessed by comparing it with several well-known distributions, including the exponential, Chris–Jerry, gamma, sine exponential, Shanker, Lindley, and X-Lindley distributions. The empirical results reveal that the QGaD provides superior fits to real-world data based on standard goodness-of-fit measures. Overall, the findings highlight the potential of the QGaD as a robust and flexible tool for modeling lifetime and reliability data. The study concludes that QGaD makes a valuable contribution to the development of statistical models, particularly in contexts that require a parsimonious yet versatile distribution.

This paper studies the exact reliability evaluation of the classical five‐component bridge network when the component lifetimes follow the Power Bilal distribution. The Power Bilal model extends the classical Bilal distribution by adding a shape parameter, which increases modeling flexibility while preserving a simple and analytically tractable survival function. Under the assumption of independent and identically distributed components, an explicit expression for the bridge‐system reliability is derived. A closed‐form expression for the mean time to failure is also obtained in terms of the lower incomplete beta function. In addition, two single‐component reinforcement strategies are investigated. It is shown analytically that, for the same improvement level, reinforcing an outer branch component always gives a larger reliability gain than reinforcing the middle component. A real data application based on waiting times of bank customers is included to assess the empirical suitability of the Power Bilal model and to compare it with standard lifetime distributions. The numerical and empirical results show that the Power Bilal distribution provides a flexible and analytically convenient framework for bridge‐network reliability analysis and for guiding targeted reliability‐improvement decisions.

This paper introduces the Rational–Saturating–Reciprocal (RSR) distribution, a flexible four-parameter lifetime model defined through a novel hazard-rate formulation on [0,∞). By combining constant, saturating, and reciprocal hazard components, the proposed model accommodates a wide range of hazard-rate shapes, including increasing, decreasing, unimodal, and bathtub patterns commonly observed in reliability and survival analysis. Its main statistical properties are established, with closed-form expressions derived for the cumulative hazard, survival, cumulative distribution, and probability density functions. Additional results for moments, the moment generating function, mean residual life, reversed hazard rate, stochastic ordering, and order statistics are also obtained. Parameter estimation is carried out using maximum likelihood, and the corresponding score functions and observed information matrix are derived. The practical usefulness of the RSR distribution is demonstrated through Monte Carlo simulations, system reliability analysis, an M/RSR/1/1 queueing model, and applications to two benchmark lifetime datasets. The results show that the proposed model provides an accurate and competitive fit, making it a valuable alternative for modeling lifetime data in reliability, survival analysis, and related stochastic applications.

Lifetime data arising in reliability, survival analysis, engineering, and environmental studies are often positive, right-skewed, and affected by early-failure or wear-out mechanisms. Classical mod...