Amari–Chentsov structure on the statistical manifold of models for accelerated life tests

Fode Zhang, Hon Keung Tony Ng (), Yimin Shi and Ruibing Wang
Additional contact information
Fode Zhang: Southwestern University of Finance and Economics
Hon Keung Tony Ng: Southern Methodist University
Yimin Shi: Northwestern Polytechnical University
Ruibing Wang: Northwestern Polytechnical University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 1, No 8, 77-105

Abstract: Abstract The invariant geometric structures on the statistical manifold under sufficient statistics have played an important role in both statistical inference and information theory. In this paper, we focus on one of the commonly used invariant geometric structures, the Amari–Chentsov structure, on a statistical manifold. The manifold is derived from statistical models for accelerated life tests (ALTs) with censoring based on the exponential family of distributions. The constant-stress ALTs and step-stress ALTs are considered. We show that the statistical manifold still belongs to the exponential family of distributions, but the cumulant generating function depends on a random variable related to the experimental design of the ALT, which is different from the usual situation. We also investigate the Bregman divergence and Riemannian metric. The relationships between the Riemannian metric and the expected Fisher information metric are studied. The dual coordinate system is studied by using the Legendre transformation. Then, the Amari–Chentsov structure is derived based on the two different coordinate systems. The methodologies are illustrated by using two distributions, the exponential and gamma distributions, in the exponential family of distributions. Finally, using the results of Fisher information metric, optimal designs of the two types of ALTs are presented with different optimal criteria. Finally, numerical examples are provided to demonstrate the practical applications of the results developed in this paper.

Keywords: Amari–Chentsov structure; Statistical manifold; Accelerated life tests; Censoring data; Bregman divergence; 53B05; 60E05; 62N05 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11749-018-0587-1 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:testjl:v:28:y:2019:i:1:d:10.1007_s11749-018-0587-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-018-0587-1

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().