: 10.62796/pijst
Dr. N.N. Limbu, PhD (Statistics), Gauhati University, Guwahati Assam
Published Date: 04-08-2025 Issue: Vol. 2 No. 8 (2025): August 2025 Published Paper PDF: Download
Abstract- The Premium Linear-Exponential (PLE) distribution is introduced as a new member of the linear-exponential family through a compound mechanism involving the Premium and Exponential distributions. This distribution generalizes the standard linear-exponential model by incorporating an additional parameter, offering greater flexibility in modeling lifetime and reliability data. The present study derives the statistical formulation of the PLE distribution and investigates its key properties, including the probability density function (PDF), cumulative distribution function (CDF), hazard rate, moments, and entropy measures. Further, the model’s quantile function, Bonferroni and Lorenz curves, and mean deviations are discussed to highlight its practical versatility. In addition to theoretical development, the PLE distribution’s applicability is evaluated using real-world datasets from the fields of engineering and biological sciences. These include failure times of turbochargers in racing vehicles and survival times of laboratory animals under infection stress. Goodness-of-fit tests, such as the Kolmogorov–Smirnov test, are employed to validate the model’s performance, demonstrating its superiority over existing distributions in capturing diverse failure behaviors including monotonic, non-monotonic, and bathtub-shaped hazard rates. The proposed distribution enhances reliability modeling by accommodating various shapes of failure rate functions depending on its parameter values. This paper concludes that the PLE distribution offers a statistically sound and practically effective approach for modeling reliability and survival data, making it a valuable addition to the growing family of flexible lifetime distributions used in engineering, medicine, and risk analysis.
Keywords-Premium Linear-Exponential Distribution; Lifetime Data; Reliability Analysis; Hazard Rate; Survival Modeling; Entropy Measures; Flexible Distributions.
Published Date: 04-08-2025 Issue: Vol. 2 No. 8 (2025): August 2025 Published Paper PDF: Download
Abstract- The Premium Linear-Exponential (PLE) distribution is introduced as a new member of the linear-exponential family through a compound mechanism involving the Premium and Exponential distributions. This distribution generalizes the standard linear-exponential model by incorporating an additional parameter, offering greater flexibility in modeling lifetime and reliability data. The present study derives the statistical formulation of the PLE distribution and investigates its key properties, including the probability density function (PDF), cumulative distribution function (CDF), hazard rate, moments, and entropy measures. Further, the model’s quantile function, Bonferroni and Lorenz curves, and mean deviations are discussed to highlight its practical versatility. In addition to theoretical development, the PLE distribution’s applicability is evaluated using real-world datasets from the fields of engineering and biological sciences. These include failure times of turbochargers in racing vehicles and survival times of laboratory animals under infection stress. Goodness-of-fit tests, such as the Kolmogorov–Smirnov test, are employed to validate the model’s performance, demonstrating its superiority over existing distributions in capturing diverse failure behaviors including monotonic, non-monotonic, and bathtub-shaped hazard rates. The proposed distribution enhances reliability modeling by accommodating various shapes of failure rate functions depending on its parameter values. This paper concludes that the PLE distribution offers a statistically sound and practically effective approach for modeling reliability and survival data, making it a valuable addition to the growing family of flexible lifetime distributions used in engineering, medicine, and risk analysis.
Keywords-Premium Linear-Exponential Distribution; Lifetime Data; Reliability Analysis; Hazard Rate; Survival Modeling; Entropy Measures; Flexible Distributions.
