Progressive censoring with fixed censoring times. Issue 3 (4th May 2019)

• Record Type: Journal Article
• Authors: Laumen, Benjamin; Cramer, Erhard
• Is Part Of: Statistics. Volume 53:Issue 3(2019)
• Page Start: 569
• Page End: 600
• Publication Date: 2019-05-04
• Subjects: Exact confidence intervals -- exponential distribution -- maximum likelihood estimation -- progressive Type-I censoring -- progressive censoring -- stochastic monotonicity; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1579817
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In this paper, we revisit the progressive Type-I censoring scheme as it has originally been introduced by Cohen [Progressively censored samples in life testing. Technometrics. 1963;5(3):327–339]. In fact, original progressive Type-I censoring proceeds as progressive Type-II censoring but with fixed censoring times instead of failure time based censoring times. Apparently, a time truncation has been added to this censoring scheme by interpreting the final censoring time as a termination time. Therefore, not much work has been done on Cohens's original progressive censoring scheme with fixed censoring times. Thus, we discuss distributional results for this scheme and establish exact distributional results in likelihood inference for exponentially distributed lifetimes. In particular, we obtain the exact distribution of the maximum likelihood estimator (MLE). Further, the stochastic monotonicity of the MLE is verified in order to construct exact confidence intervals for both the scale parameter and the reliability.