On the distribution of the estimated mean from nonstandard mixtures of distributions
The distribution of the estimated mean of the nonstandard mixture of distributions that has a discrete probability mass at zero and a gamma distribution for positive values is derived. Furthermore, for the studied nonstandard mixture of distributions, the distribution of the standardized statistic (estimator - true mean)/standard deviation of estimator is derived. The results are used to study the accuracy of the confidence interval for the mean based on a large sample approximation. Quantiles for the standardized statistic are also calculated.