Sequential estimation of the mean of a negative binomial distribution

Abstract

A procedure is proposed to estimate the mean of a negative binomial distribution when the value of the exponent, k , is known. The procedure is to continue sampling until the sample path crosses a rectangular hyperbola whose centre determines the precision of the estimate. An approximation to the distribution of the estimate is obtained and it is shown that this distribution is close to log normal with known variance independent of the sample size. The effect of imperfect information on k is investigated. Comparisons are made with other procedures including the variance-stabilizing logarithmic transformation.