Statistical inferences for parameters of zero-inflated skewed distributions

Abstract

The Delta-Inverse Gaussian (delta-IG) distribution is a statistical distribution that incorporates a delta parameter to improve the inverse Gaussian distribution. This delta parameter allows modifications to the distribution's skewness or kurtosis, making it easier to handle data with different shapes or variability patterns in circumstances with an excess of zeros and substantially skewed data. In this thesis, confidence intervals will be used to estimate delta-IG distributions for single- and two-parameter simulations. The generalized confidence interval, adjusted generalized confidence interval, bootstrap percentile confidence interval, fiducial confidence interval, fiducial highest posterior density confidence interval, Bayesian credible interval, Bayesian highest posterior density credible interval, method of variance estimates recovery, and normal approximation will be used as estimation methods. The purpose of this thesis is to calculate the confidence intervals for the function (the single, difference, and ratio) of the variance of the delta-IG distributions. Next, create the confidence intervals for the function of coefficient of variation (CV) for the delta-IG distributions, as well as the confidence intervals of common CV for the delta-IG distributions and the simultaneous confidence intervals for difference of CV for the delta-IG distributions. The optimal confidence interval has a coverage probability better than 0.95 and the smallest Monte Carlo simulation average width. To verify the recommended methods, all methods were tested on traffic fatality data.