Estimation of the Parameters of the Generalized Inverted Exponential Distribution with Progressive type I Interval Censored Data.

In this article, we study estimation methodologies for parameters of a generalized inverted exponential distribution based on different estimation methods using progressively type I interval censored data. In this approach, besides conventional maximum likelihood estimation, mid-point method, probability plot method and method of moments are proposed for parameter estimation. To obtain maximum likelihood estimates, we use Newton-Raphson, expectation-maximization and stochastic expectation-maximization methods. Moreover, the approximate confidence intervals of the parameters are obtained via the inverse of the observed information matrix. In addition, percentile bootstrap technique is utilized to compute confidence intervals. Numerical comparisons are presented of the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, survival times of guinea pigs injected with different doses of tubercle bacilli data is considered to show the applicability of the proposed methods. Finally, different methods for determining the inspection times and optimal censoring planes are studied. [ABSTRACT FROM AUTHOR]