A Novel Extended of the Exponential Distribution with Modeling Complex Lifetime and Environmental Data

Probability distributions are widely utilized throughout several domains of life, particularly for studying environmental, biology, medicine, economics, insurance, hydrology, and many more. Standard probability distributions have been utilized in practice for an extended period. In this work, we proposed a continuous probability distribution according to the Ramos Louzada logic called the Ramos Louzada Exponential model with two parameters. The proposed model is more flexible in modeling several types of datasets, such as skewed, complex, asymmetrical, and symmetric. 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, various 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 model's utility was demonstrated by the use of three real-life data sets taken from the lifetime and environmental fields.