From B-spline representations to gamma representations in hybrid censoring

Julian Górny and Erhard Cramer ()
Additional contact information
Julian Górny: RWTH Aachen University
Erhard Cramer: RWTH Aachen University

Statistical Papers, 2019, vol. 60, issue 4, No 6, 1119-1135

Abstract: Abstract We establish an identity that relates B-spline functions to linear combinations of gamma density functions. Utilizing this connection, we illustrate that, for exponentially distributed lifetimes, the distribution of the MLE in various hybrid censoring schemes can be expressed in terms of gamma density functions with simple weights. As an example, representations for the density functions in the case of Type-I sequential, Type-II progressive hybrid, generalized Type-I progressive hybrid, and generalized Type-II progressive hybrid censoring schemes are presented. It turns out that the representations arising from the spacings’ based approach introduced in Cramer and Balakrishnan (Stat Methodol 10:128–150, 2013) are more compact than those available in the literature so far.

Keywords: Hybrid censoring; Progressive censoring; Type-I censored sequential k-out-of-n systems; Type-I progressive hybrid censoring; Adaptive Type-I progressive hybrid censoring; Type-II progressive hybrid censoring; Generalized Type-I progressive hybrid censoring; Generalized Type-II progressive hybrid censoring; B-spline; Divided differences; Exponential distribution; Gamma distribution; Simple step-stress model (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-016-0866-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0866-4

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-016-0866-4

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().