On Sampling Design Issues when Dealing with Zeros

Abstract

We study the problem of identifying payment errors in a population of claims containing “zeros,” that is, claims that are error-free, and the advantage of using proportional stratified sampling versus simple random sampling. The classical model assumes that the payment, Y, is multiplied by a random variable, X, with probability p(Y) of being in error. Traditionally, p(Y) is assumed to be constant. In this article we focus on the model where p(Y) is a two-valued step function, but we also consider a model where p(Y) is a continuous exponential function. We assume that Y has a gamma distribution, a good approximation in many real-world populations of claim payments. We consider the use of proportional stratification with two strata and introduce a criterion of goodness, G, as the gain in reducing the coefficient of variation by use of proportional stratification relative to ignoring the strata and applying simple random sampling.