Résumé: This paper introduces a new probability model, the A special mixture of exponential and gamma models generate Xexponential model. The study explores the mathematical properties of this new model, including the moment generation function, moments, mode, and quantile function. The research evaluates various estimators to estimate the unknown parameter of the distribution using a Monte Carlo simulation. Also, the goodness-of-fit test is provided for this model. Additionally, the flexibility of the Xexponential model is compared to that of other commonly used models, such as gamma, exponential, Lindley, Shanker, Akash, Zeghdoudi, and Chris-Jerry, by applying the model to a real data set. The results indicate that the proposed model provides more flexibility and a better fit than other models. These findings suggest that the Xexponential model could be useful in modeling real-life data and may warrant further

Résumé: Modeling and analyzing life expectancy data is essential in many fields, including actuarial science, management, engineering, medicine, physics, biology, hydrology, and computer science. Classical probability distributions have been used to handle data sets of various sizes. However, significant problems arise when real-world data do not fit any classical or conventional probability model. Therefore, it is important to improve the flexibility of existing probability models by introducing a combination of two distributions or introducing additional parameters. This work presents a new XLindley distribution with a single parameter. Both symmetric and left-skewed data can be used with the proposed model. We generate statistical features such as mode , mean, variance and moments functions to accurately represent the utility of the proposed distribution. We compute parameters using maximum likelihood estimation

Résumé: In Reliability, the distributions with unimodal or the so-called -shape hazard functions are used quiet often. Mostly people use log-normal, log-logistic and inverse Gaussian distributions. In this paper, we consider also an application of the inverse Gaussian, log-normal and log-logistic distribution in the reliability analysis of redundant system with one main unit and stand-by units. Properties of the point estimators and confidence intervals are studied.