Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

Abstract

PurposeThe 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/approachWe 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.FindingsWe 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/valueThis 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.