Generalized Confidence Intervals for Zero-Inflated Pareto Distribution

This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.

Generalized Confidence Intervals for Intra- and Inter-subject Coefficients of Variation in Linear Mixed-effects Models

Linear mixed-effects models are linear models with several variance components. Models with a single random-effects factor have two variance components: the random-effects variance, i. e., the inter-subject variance, and the residual error variance, i. e., the intra-subject variance. In many applications, it is practice to report variance components as coefficients of variation. The intra- and inter-subject coefficients of variation are the square roots of the corresponding variances divided by the mean. This article proposes methods for computing confidence intervals for intra- and inter-subject coefficients of variation using generalized pivotal quantities. The methods are illustrated through two examples. In the first example, precision is assessed within and between runs in a bioanalytical method validation. In the second example, variation is estimated within and between main plots in an agricultural split-plot experiment. Coverage of generalized confidence intervals is investigated through simulation and shown to be close to the nominal value.