Inference Under Right Censoring in a Discrete Setup

Abstract

In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/θ₁ and 1/θ₂, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior Regret Gamma Minimax estimators of the parameters for the two cases when the prior distributions are dependent and independent, assuming a squared error loss function. We then discuss the Proportional Hazard model, and obtain Maximum Likelihood estimators of the unknown parameters and derive the Bayes estimators assuming squared error loss using Markov Chain Monte Carlo methods.

Keywords:

• Discrete right censoring
• Geometric distribution
• Posterior regret gamma minimax
• Proportional hazard model

Mathematics Subject Classification:

• Primary 62N01, 62N02
• Secondary 62C10, 62C15, 62F15, 62F35

Acknowledgment

The authors are grateful to the Editor, referees, and Professor Mahbanoo Tata for making many helpful comments and suggestions. Ahmad Parsian's research supported by a grant of Research Council of the University of Tehran.

Notes

*In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

*In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

*In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

*In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

*The entries in the first and second rows of each box are, respectively, the estimated MSE of the estimate and the corresponding bias.

*The entries in the first and second rows of each box are, respectively, the estimated MSE of the estimate and the corresponding bias. The third row indicates number of times that z = n or(2v − n)z > v ² for the actual data.