, Volume 81, Issue 8, pp 1005–1024 | Cite as

On purely sequential estimation of an inverse Gaussian mean

  • Sudeep R. BapatEmail author


The first part of this paper deals with developing a purely sequential methodology for the point estimation of the mean \(\mu \) of an inverse Gaussian distribution having an unknown scale parameter \(\lambda \). 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 \(\omega \). 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 \(\mu \), assuming that the scale parameter \(\lambda \) 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.


Fatigue life Inverse Gaussian Purely sequential Fixed-accuracy intervals Point estimation First-order asymptotic efficiency First-order asymptotic consistency 

Mathematics Subject Classification

62L12 62L05 62F12 62P30 



The author would like to sincerely thank the editor in chief, Dr. Hajo Holzmann and the anonymous referee for their valuable and constructive comments which greatly improved an earlier manuscript.

Compliance with ethical standards

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and Applied Probability, South HallUniversity of California, Santa BarbaraSanta BarbaraUSA

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