On purely sequential estimation of an inverse Gaussian mean

Abstract

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.