Estimation and testing procedures of the reliability functions of generalized inverted scale family of distributions

ABSTRACT

We consider here the generalized inverted scale family of distributions proposed by Potdar and Shirke [Inference for the parameters of generalized inverted family of distributions. ProbStat Forum. 2013;06:18–28] by zeroing in on two measures of reliability, $R\left(t\right)=P(X>t)$ and $\mathcal{P}=P(X>Y)$, based on Type II censoring and the sampling scheme of Bartholomew [The sampling distribution of an estimate arising in life testing. Technometrics. 1963;5:361–374]. Thereafter, we develop point estimators of powers of α, $R\left(t\right)$ and $\mathcal{P}$; and develop uniformly minimum variance unbiased (UMVU) estimators and maximum likelihood (ML) estimators. A new technique of obtaining these estimators is introduced. Exact confidence intervals for the parameter α, $R\left(t\right)$ and $\mathcal{P}$ are also constructed based on Type II censoring. Then we derive testing procedures for the hypotheses related to different parametric functions. Finally, we compare these results using the Monte Carlo simulation method.

KEYWORDS:

• Point estimation
• testing procedures
• Type II censoring
• sampling scheme of Bartholomew
• Monte Carlo simulation method

Acknowledgements

The authors are extending gratitude to the reviewers and the associated editors for their insightful reading and precious comments that led to substantial improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.