Approximate Confidence Intervals for a Parameter of the Negative Hypergeometric Distribution

• Activity Number: 413
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Lei Zhang and William D. Johnson*+
• Companies: Mississippi State Department of Health and Pennington Biomedical Research Center
• Keywords: Confidence interval ; Empirical coverage probability ; Inverse sampling ; Large sample theory ; Negative hypergeometric distribution ; Unbiased estimator

Abstract

The negative hypergeometric distribution (NHD) is of interest in applications of inverse sampling without replacement from a finite population. 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. Assuming the total number of units in the population is known but the number of each type is not, we investigate the maximum likelihood estimator (MLE) and an unbiased estimator for the unknown parameter. We use Taylor's series to develop five approximations for the variance of the parameter estimators. We then propose five large sample confidence intervals (CIs) for the parameter. Based on these results, we simulated a large number of samples from various NHDs to investigate performance in terms of empirical probability of parameter coverage and CI length. The unbiased estimator is a better point estimator relative to the MLE as evidenced by empirical estimates of closeness to the true parameter. CIs based on the unbiased estimator tended to be shorter than two competitors because of its relatively small variance estimator but at a slight cost in terms of coverage probability.