Estimation in Simple Step-Stress Model for the Marshall-Olkin Generalized Exponential Distribution under Type-I Censoring

This paper considers the simple step-stress model from the Marshall-Olkin generalized exponential distribution when there is time constraint on the duration of the experiment. The maximum likelihood equations for estimating the parameters assuming a cumulative exposure model with lifetimes as the distributed Marshall-Olkin generalized exponential are derived. The likelihood equations do not lead to closed form expressions for the maximum likelihood estimators (MLEs)، and they need to be solved by using an iterative procedure. We then evaluate the properties of MLEs through the mean squared error، relative absolute bias and relative error. We also derive confidence intervals for the parameters using asymptotic distributions of the MLEs and the parametric bootstrap methods. Finally، an example is presented to illustrate the discussed methods of asymptotic and bootstrap confidence intervals.