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The Birnbaum-Saunders distribution is widely used in fields such as survival analysis. In this paper, we use a new method to construct confidence intervals for the shape parameter of the Birnbaum-Saunders distribution and find it superior to some existing methods. Our method can be called the 'joint pivot method' as we obtain the confidence interval by uniting two pivots. Furthermore, we find that the joint pivot method can also be used to solve the Behrens-Fisher problem. Simulation studies show that the joint pivot method is comparable with some commonly practiced ones. Finally, we analyse two real data sets to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probabilitypof the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method. [ABSTRACT FROM PUBLISHER]

Birnbaum–Saunders (BS) distribution is widely used in reliability applications to model failure times. For several samples from possible different BS distributions, to prevent wrong conclusions in any further analysis, it is of importance to accompany a formal comparison for characteristic quantities of the distributions, including mean, quantile and reliability function difference. To this end, two test statistics, which are respectively based on the exact generalizedp-value approach and the Delta method, are proposed and their behaviours are investigated. Simulation studies are carried out to examine the size and power performance of the newly proposed statistics. An interesting phenomenon is that in the finite sample simulations we conduct, the Delta method-based test almost uniformly outperforms the generalizedp-value-based test although its sampling null distribution is simulated by Monte Carlo method. This might suggest that the sampling null distribution of the Delta method-based test statistic would have a fast convergence to its limit. The tests are also applied to analyse a real example on the fatigue life of 6061-T6 aluminium coupons for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we propose a test on the parametric form of the coefficient functions in the varying coefficient model with missing response. Two groups of completed data sets are constructed by using imputation and inverse probability weighting methods respectively. By noting that the coefficient part can be a regression function for a specific model, we construct two empirical process-based tests. The asymptotical distributions of the proposed tests under null and local alternative hypothesis are investigated respectively. Simulation study is carried out to show the power performance of the test. We illustrate the proposed approaches with an environmental data set. [ABSTRACT FROM AUTHOR]

In this study, we consider the testing problem about the null hypothesis that the nonlinear part in the partial linear regression model with missing response at random is a parametric function or not against the alternative that it is nonparametric. By imputation and inverse probability weighting methods, we then construct two completed data sets. Two empirical process-based tests, from these completed data sets, are introduced. Under the null hypothesis and local alterative hypotheses, the limiting null distributions and power study of the test statistics are, respectively, investigated. A nonparametric Monte Carlo test procedure, which can automatically make the test procedure scale-invariant even when the test statistics are not scale-invariant, is applied to approximate the limiting null distributions of the test statistics. Simulation study is carried out to examine the performance of the tests. We illustrate the proposed method with a real data set on monozygotic twins. [ABSTRACT FROM PUBLISHER]

The partial linear regression model is wildly used due to its well established theories, flexibility and easy interpretation. This paper aims to investigate the specification test of nonparametric component in partial linear model with response missing at random. Two quadratic conditional moment tests are proposed and both two test statistics own limiting normal distributions when nonparametric component is correctly specified. Our tests’ virtue is that p -values can be easily determined based on limiting null distributions which are intractable for existing tests. The tests can detect the alternative hypotheses distinct from the null hypothesis at the optimal nonparametric rate for local smoothing-based methods. Simulation studies reveal that our tests can control type I error well and have excellent power performance. A HIV clinical trial real data is analyzed for illustrating our methods. [ABSTRACT FROM AUTHOR]

The Wilcoxon–Mann–Whitney test is designed to test homogeneity of two random samples in the univariate case. It is very powerful to detect location shifts yet may lose power completely when there exist scale differences. We generalize the classic Wilcoxon–Mann–Whitney test through using pairwise distances of all observations. The generalized test can be readily used even when the random observations are multivariate. It is also very powerful in the presence of scale differences. The generalized test is in spirit to compare difference between the distribution functions of two random samples. It is m n / (m + n) -consistent under the strong null and local alternatives, and root- m n / (m + n) -consistent under fixed alternatives, where m , n stand for the respective sizes of the two random samples. The power of the generalized test is asymptotically independent of m / n , the size ratio of the two random samples. This indicates that the generalized test has nontrivial power as long as the sample sizes are not extremely unbalanced. We demonstrate the theoretical properties of our improved rank-based two-sample test through comprehensive numerical studies. [ABSTRACT FROM AUTHOR]