Estimation for exponential distribution based on competing risk middle censored data

For a general censoring scheme called middle censoring scheme which was proposed by Jammalamadaka and Mangalam (2003) in nonparametric set up. In this article, point and interval estimation problems are considered for the exponential distribution when the failure data is middle censored with two independent competing failure risks. Different methods are introduced to estimate the unknown model parameters such as maximum likelihood estimation, midpoint approximation, equivalent quantities estimation. The Bayesian estimation is also considered with gamma priors. Two numerical examples are analyzed to show the performance of the proposed methods.