Jackknife empirical likelihood for the mean of a zero-and-one inflated population

In many statistical analysis, a finite population may contain a large proportion of zero-and-one values that make the population distribution severely skew. Confidence intervals based on a normal approximation (NA) for such data may have low coverage probabilities. In this paper, we apply the methods of jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) to discuss the confidence intervals for the mean of zero-and-one inflated population. Asymptotic distributions of the likelihood-type statistics are studied. Simulations are conducted to compare coverage probabilities with other methods under different distributions. Real data is given to illustrate the procedure of proposed methods.