Statistical Inference for Multicomponent System Stress-Strength Model with Bounded Strengths

In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well-resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

Statistical inference on mixing proportion

In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.