A Novel Quantile-Transformed Exponential Distribution With Applications in Reliability and Survival Analyses

This paper aims to derive a novel quantile-transformed exponential distribution (QTED) as a flexible extension of the exponential distribution. The need for this study arises from the limitation of the exponential distribution in modeling real-world data with nonconstant hazard rates. The proposed distribution is constructed using a quantile transformation approach. Important statistical properties of the distribution are derived. Parameters of the distribution were estimated using the maximum likelihood method. Using simulation studies, random samples are generated from the new distribution to show how ideal data look like. With practical data from diverse sources such as health and technology, the applicability of new distribution to real data is demonstrated. The results indicate that the proposed distribution provides a better fit than the existing distributions. The findings suggest that the new distribution is capable of capturing a variety of hazard function behaviors, including increasing, decreasing, and bathtub-shaped patterns, making it particularly suitable for reliability and survival analyses. Overall, the proposed distribution offers a flexible and effective alternative for analyzing lifetime data characterized by complex hazard structures and distributional asymmetry.