Estimation of the population total when the population size is unknown

This paper considers the problem of estimating the population total when the population size is unknown. A sampling design, in which units are selected with equal probability, are sequentially marked and then returned back until a fixed number of repetitions occur, has been considered. This allows the estimation of the population size as well as the population total. A formula for confidence intervals for the population total is derived along with an approximately unbiased estimator for the variance of the estimator of the population total.