Bootstrapping with R to Determine Variances of Mixture Model Estimates in Predicting Confidence Intervals for Population Sizes

It is not easy to find the variance estimates of mixture model via the theoretical derivation directly. Instead, bootstrapping denoting a resampling technique from an original sample dataset with replacement allocation is used to calculate variances of mixture estimates of zero-truncated Poisson distributions in a prediction of population size and its confidence interval. The application is the estimation of the number of drug (opium) users in Thailand 2007 under surveillance data of counts of treatment episodes in a case. The results indicated that there were 3,262 observed opium cases who received treatments, the estimate of the unobserved number of opium users without receiving any treatment was 3,931, leading to total population size estimate of 7,193 opium users. The 95% confidence intervals as a by-product of bootstrapping were 6,674-7,712 under bootstrap normal base, 6,782-7,761 under bootstrap 95% percentiles, and 6,626-7,605 under bootstrap t intervals. Bootstrapping algorithm with R program is available here.