On purely sequential estimation of an inverse Gaussian mean

Sudeep R. Bapat ()
Additional contact information
Sudeep R. Bapat: University of California, Santa Barbara

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 8, No 5, 1005-1024

Abstract: Abstract The first part of this paper deals with developing a purely sequential methodology for the point estimation of the mean $$\mu $$ μ of an inverse Gaussian distribution having an unknown scale parameter $$\lambda $$ λ . We assume a weighted squared error loss function and aim at controlling the associated risk function per unit cost by bounding it from above by a known constant $$\omega $$ ω . We also establish first-order and second-order asymptotic properties of our stopping rule. The second part of this paper deals with obtaining a purely sequential fixed accuracy confidence interval for the unknown mean $$\mu $$ μ , assuming that the scale parameter $$\lambda $$ λ is known. First-order asymptotic efficiency and asymptotic consistency properties are also built of our proposed procedures. We then provide extensive sets of simulation studies and real data analysis using data from fatigue life analysis to show encouraging performances of our proposed stopping strategies.

Keywords: Fatigue life; Inverse Gaussian; Purely sequential; Fixed-accuracy intervals; Point estimation; First-order asymptotic efficiency; First-order asymptotic consistency; 62L12; 62L05; 62F12; 62P30 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00184-018-0665-0 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:metrik:v:81:y:2018:i:8:d:10.1007_s00184-018-0665-0

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-018-0665-0

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().