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.

Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.

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.

Statistical procedures for testing hypotheses of equivalence in the safety evaluation of a genetically modified crop

SUMMARYSafety evaluation of a genetically modified crop entails assessing its equivalence to conventional crops under multi-site randomized block field designs. Despite mounting petitions for regulatory approval, there lack a scientifically sound and powerful statistical method for establishing equivalence. The current paper develops and validates two procedures for testing a recently identified class of equivalence uniquely suited to crop safety. One procedure employs the modified large sample (MLS) method; the other is based on generalized pivotal quantities (GPQs). Because both methods were originally created under balanced designs, common issues associated with incomplete and unbalanced field designs were addressed by first identifying unfulfilled theoretical assumptions and then replacing them with user-friendly approximations. Simulation indicated that the MLS procedure could be very conservative in many occasions irrespective of the balance of the design; the GPQ procedure was mildly liberal with its type I error rate near the nominal level when the design is balanced. Additional pros and cons of these two procedures are also discussed. Their utility is demonstrated in a case study using summary statistics derived from a real-world dataset.

Inference for One-Way ANOVA with Equicorrelation Error Structure

We consider inferences in a one-way ANOVA model with equicorrelation error structures. Hypotheses of the equality of the means are discussed. A generalizedF-test has been proposed by in the literature to compare the means of all populations. However, they did not discuss the performance of that test. We propose two methods, a generalized pivotal quantities-based method and a parametric bootstrap method, to test the hypotheses of equality of the means. We compare the empirical performance of the proposed tests with the generalizedF-test. It can be seen from the simulation results that the generalizedF-test does not perform well in terms of Type I error rate, and the proposed tests perform much better. We also provide corresponding simultaneous confidence intervals for all pair-wise differences of the means, whose coverage probabilities are close to the confidence level.