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

Abstract

In this article, we study estimation methodologies for parameters of a generalized inverted exponentialdistribution based on different estimation methods using progressively type I interval censored data. Inthis approach, besides conventional maximum likelihood estimation, mid-point method, probability plotmethod and method of moments are proposed for parameter estimation. To obtain maximum likelihood esti-mates, we use Newton-Raphson, expectation-maximization and stochastic expectation-maximization meth-ods. Moreover, the approximate confidence intervals of the parameters are obtained via the inverse of theobserved information matrix. In addition, percentile bootstrap technique is utilized to compute confidenceintervals. Numerical comparisons are presented of the proposed estimators using Monte Carlo simulation-s. To demonstrate the proposed methodology in a real-life scenario, survival times of guinea pigs injectedwith 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.Estimation of the Parameters of the Generalized Inverted ExponentialDistribution with Progressive type I Interval Censored Data