The Topp-Leone G- Rayleigh Rayleigh Distribution: Properties and Applications

Abstract

The (Topp Leone) distribution as well as the (Rayleigh) distribution are among the continuous distributions that are widely used in the analysis of survival and failure functions. This study used rule called the (Topp Leone Generator family) to make a new probability distribution it was called the (Topp Leon G-Rayleigh Rayleigh (TLG-RR)) distribution. By adding one of the shape parameters for an existing probability distribution, it called(Expanding Rayleigh distribution).This study will extract the basic properties of the distribution and estimate its parameters using estimation methodslike method of greatest possibility (MLE), method of weighted least squares (WLS) and method of Shrinkage to estimate parameters and reliability function. The study concluded that the proposed distribution(TLG-RR) is the best probability distribution in representing the real data used in the study.And best way to estimate the reliability function it is shrinkage method.