Stochastically increasing grouped data using the MLE of mean of the generalized exponential distribution

The generalized exponential distribution with two parameters has the verity of applications. In literature, the generalized exponential distribution mean are obtained through maximum likelihood estimators based on various data structures. However, the order preserving property of generalized exponential distribution estimators are not found in the literature. This property discusses in this article. Coupling method is used to check the stochastic increment of grouped data using the generalized exponential distribution. The parameters are estimated through maximum likelihood estimation. The distances are decreasing lies between the inspection times are stochastically ordered. The assumptions of monotonicity are dropped in successive distances. The Markove property is used to attain the assumptions of monotonicity. Subject Classification: (2010) 60G20.