Résumé: In order for X and Y to be independent, this study addresses the problem of estimating Reliability P[Y< X ] where Y has a Zeghdoudi distribution with parameter a, X has a Zeghdoudi distribution with one outlier present and parameter c, and the remaining random variables (n-1) are from a Zeghdoudi distribution with parameter b. A few simulation study findings and the maximum likelihood estimate of R, are provided. We also present some results about fuzzy dependability. Finally, using actual data on the survival durations (in days) of 72 Algerians infected with the Corona virus, we demonstrate how the Zeghdoudi distribution may be applied to other distributions to demonstrate the adaptability of this distribution.

Résumé: This study designs a new lifetime distribution by compounding the exponential and Lindley distributions. The new distribution has decreasing hazard rates shapes, which fit many applications in reliability and survival analysis. Different numerical properties of moment method and maximum likelihood estimation are identified. The parameter estimation of the new distribution is explained by estimation methods and to recommend its performance, a simulation is proposed. This new model is compared by well-known one and two parameters distributions using two real-life data sets.

Résumé: In this paper, a new geometrical approach of Chain Ladder method aspect is given. More precisely, development factors (k_j ) are estimated by graphical technique, therefore it is required to compute the tangents for each development year j, and then the lower circles are estimated using observed circles and tangents. In order to validate the proposed approach a numerical application is conducted, the obtained results are similar to those computed by chain-Ladder method and stochastic incremental approach. Moreover, some examples are given to illustrate and show the effectiveness of the proposed approach.