Purely Sequential and k-Stage Procedures for Estimating the Mean of an Inverse Gaussian Distribution

Ajit Chaturvedi, Sudeep R. Bapat and Neeraj Joshi ()
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Ajit Chaturvedi: University of Delhi
Sudeep R. Bapat: University of California
Neeraj Joshi: University of Delhi

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 1193-1219

Abstract: Abstract In the first part of this paper, we propose purely sequential and k-stage (k ≥ 3) procedures for estimation of the mean μ of an inverse Gaussian distribution having prescribed ‘proportional closeness’. The problem is constructed in such a manner that the boundedness of the expected loss is equivalent to the estimation of parameter with given ‘proportional closeness’. We obtain the associated second-order approximations for both the procedures. Second part of this paper deals with developing the minimum risk and bounded risk point estimation problems for estimating the mean μ of an inverse Gaussian distribution having unknown scale parameter λ. We propose an useful family of loss functions for both the problems and our aim is to control the associated risk functions. Moreover, we establish the failure of fixed sample size procedures to deal with these problems and hence propose purely sequential and k-stage (k ≥ 3) procedures to estimate the mean μ. We also obtain the second-order approximations associated with our sequential procedures. Further, we provide extensive sets of simulation studies and real data analysis to show the performances of our proposed procedures.

Keywords: Bounded risk; Inverse Gaussian distribution; k-stage procedure; Minimum risk; Point estimation; Proportional closeness; Purely sequential procedure; Second-order approximations; Useful family of loss functions; 62L05; 62L12; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-019-09765-x

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