A novel extension of the exponential distribution with application in modeling complex lifetime and environmental data

Probability distributions are widely utilized throughout several domains of life, particularly for studying data sets from environmental science, biology, medicine, economics, insurance, and many more. Standard probability distributions have been utilized in practice for an extended period. In this work, we proposed a continuous probability distribution based on the Ramos Louzada logic called the Ramos Louzada Exponential model with two parameters. The significance of the proposed model lies in its ability to effectively analyze the phenomena observed in nature. Its utility spans multiple disciplines. In particular, these distributions have demonstrated considerable efficacy in data modeling. The study presents some statistical and mathematical characteristics of the new distribution, such as the ordinary moment, the quantile function, the mean, the variance, and the moment generating function. To ensure precise parameter estimation, two estimation methods are evaluated, including maximum likelihood and Bayesian procedures under three suggested loss functions, accompanied by a simulation study that confirmed the reliability and consistency of the two proposed estimators. The performance of the estimators is evaluated through average estimate and mean square error. The utility of the model was demonstrated using three real-life data sets taken from the lifetime and environmental fields. Employing a meticulous comparative evaluation through an array of goodness-of-fit metrics, including Akaike Information Criterion, Correction Akaike Information Criterion (), Hannan-Quin Information Criterion, Bayesian Information Criterion, Kolmogorov-Smirnov () statistics with its associated P-values, the proposed model consistently surpassed traditional competing models such as the generalized Rayleigh, truncated Poisson exponential, alpha power transformed exponential, extended exponential, gamma, Weibull, and two parameters Mira distributions. Based on ((), p-values) [(0.1206,0.5640), (0.1002, 0.62), and (0.1121, 0.2414)] for the three proposed datasets, we observe that the proposed distribution offers optimal fitting compared to other rival distributions.