Performance of Interval Estimators for the Inverse Hypergeometric Distribution.

The inverse hypergeometric distribution is of interest in applications of inverse sampling without replacement from a finite population where a binary observation is made on each sampling unit. Thus, sampling is performed by randomly choosing units sequentially one at a time until a specified number of one of the two types is selected for the sample. Assuming the total number of units in the population is known but the number of each type is not, we consider the problem of estimating this parameter. We use the Delta method to develop approximations for the variance of three parameter estimators. We then propose three large sample confidence intervals for the parameter. Based on these results, we selected a sampling of parameter values for the inverse hypergeometric distribution to empirically investigate performance of these estimators. We evaluate their performance in terms of expected probability of parameter coverage and confidence interval length calculated as means of possible outcomes weighted by the appropriate outcome probabilities for each parameter value considered. The unbiased estimator of the parameter is the preferred estimator relative to the maximum likelihood estimator and an estimator based on a negative binomial approximation, as evidenced by empirical estimates of closeness to the true parameter value. Confidence intervals based on the unbiased estimator tend to be shorter than the two competitors because of its relatively small variance but at a slight cost in terms of coverage probability. [ABSTRACT FROM AUTHOR]