Negative Binomial Marshall–Olkin Rayleigh Distribution and Its Applications

Abstract A generalization of the Marshall–Olkin family of distributions is developed using negative binomial compounding instead of geometric compounding where addition is replaced by minimum of a random number of observations X1,X2,...,XN. Here, we consider the Rayleigh distribution and extend it to obtain a Negative Binomial Marshall–Olkin Rayleigh Distribution. Various properties of the new family are investigated. Maximum likelihood estimates are obtained. The use of the model in lifetime modeling is established by fitting it to a real data set on remission times of bladder cancer patients. Also we try to develop a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes governed by this distribution.