In this article, we develop two-stage, three-stage, and accelerated sequential procedures for the point estimation of the mean μ of an inverse Gaussian distribution when the scale parameter λ is unknown. Both minimum risk and bounded risk estimation problems are considered subject to a weighted squared error loss function. We aim at controlling the associated risk functions for all three procedures. Second-order approximations are obtained for the proposed procedures.

In this paper, we develop purely sequential, two-stage, three-stage, and “accelerated” sequential procedures for the point estimation of the location of negative exponential distribution having an unknown scale parameter. We do minimum risk point estimation by using all four sequential procedures mentioned above. In addition, we do bounded risk point estimation by using three-stage and “accelerated” sequential procedures. Consideration is given to a modified LINEX loss function. We aim at controlling the associated risk functions for all the procedures. Second-order approximations are obtained for the proposed procedures. We also discuss first-order properties for purely sequential procedure.

This paper deals with developing an improved accelerated sequential procedure to estimate the unknown mean μ of an inverse Gaussian distribution, when the scale parameter λ also remains unknown. The problems of minimum risk and bounded risk point estimation are handled. Consideration is given to a weighted squared-error loss function. Our aim is to control the associated risk functions and obtain the second-order asymptotics as well. Further, we establish the superiority of this improved accelerated sequential sampling design over the Hall's accelerated sequential procedure in estimating an inverse Gaussian mean. Appropriate simulations and real data examples are also provided in support of the encouraging performance of our proposed methodology.

Purpose: The purpose of this paper is to develop optimal estimation procedures for the stress-strength reliability (SSR) parameter R = P(X > Y) of an inverse Pareto distribution (IPD).Design/methodology/approach: We estimate the SSR parameter R = P(X > Y) of the IPD under the minimum risk and bounded risk point estimation problems, where X and Y are strength and stress variables, respectively. The total loss function considered is a combination of estimation error (squared error) and cost, utilizing which we minimize the associated risk in order to estimate the reliability parameter. As no fixed-sample technique can be used to solve the proposed point estimation problems, we propose some “cost and time efficient” adaptive sampling techniques (two-stage and purely sequential sampling methods) to tackle them.Findings: We state important results based on the proposed sampling methodologies. These include estimations of the expected sample size, standard deviation (SD) and mean square error (MSE) of the terminal estimator of reliability parameters. The theoretical values of reliability parameters and the associated sample size and risk functions are well supported by exhaustive simulation analyses. The applicability of our suggested methodology is further corroborated by a real dataset based on insurance claims.Originality/value: This study will be useful for scenarios where various logistical concerns are involved in the reliability analysis. The methodologies proposed in this study can reduce the number of sampling operations substantially and save time and cost to a great extent.