Statistical Methodology最新文献

In this paper, the estimation of the stress–strength reliability $Pr(X>Y)$ based on upper record values is considered when $X$ and $Y$ are independent random variables from a two-parameter bathtub-shaped lifetime distribution with the same shape but different scale parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimator and the exact confidence intervals of stress–strength reliability are obtained when the shape parameter is known. When the shape parameter is unknown, we obtain the MLE, the asymptotic confidence interval and some bootstrap confidence intervals of stress–strength reliability. In this case, we also apply the Gibbs sampling technique to study the Bayesian estimation of stress–strength reliability and the corresponding credible interval. A Monte Carlo simulation study is conducted to investigate and compare the performance of the different proposed methods in this paper. Finally, analysis of a real data set is presented for illustrative purposes.

The odds ratio is the predominant measure of association in $2\times 2$ contingency tables, which, for inferential purposes, is usually considered on the log-scale. Under an information theoretic set-up, it is connected to the Kullback–Leibler divergence. Considering a generalized family of divergences, the $\varphi$ divergence, alternative association measures are derived for $2\times 2$ contingency tables. Their properties are studied and asymptotic inference is developed. For some members of this family, the estimated association measures remain finite in the presence of a sampling zero while for a subset of these members the estimators of these measures have finite variance as well. Special attention is given to the power divergence, which is a parametric family. The role of its parameter $\lambda$, in terms of the asymptotic confidence intervals’ coverage probability and average relative length, is further discussed. In special probability table structures, for which the performance of the asymptotic confidence intervals for the classical log odds ratio is poor, the measure corresponding to $\lambda =1/3$ is suggested as an alternative.

In this paper, we propose a new two-sample distribution-free procedure for testing group-by-time interaction effect in repeated measurements from a linear mixed model setting. The test statistic is based on the maximum difference of partial sums (MDPS) over time points between the two groups. Although the test has a biomedical focus, it can be applied in fields that the study is designed and monitored to be balanced and complete with equal sample sizes as would be generally done in a controlled experiment. The asymptotic null distribution of the test statistic was also derived based on the maxima of Brownian bridge under two different conditions. The simulations revealed that MDPS performed markedly better than the commonly used unstructured multivariate approach (UMA) to profile analysis. However, the empirical powers of MDPS test were convincingly close to those of the best-fitting linear mixed model (LMM).

Poisson or zero-inflated Poisson models often fail to fit count data either because of over- or underdispersion relative to the Poisson distribution. Moreover, data may be correlated due to the hierarchical study design or the data collection methods. In this study, we propose a multilevel zero-inflated generalized Poisson regression model that can address both over- and underdispersed count data. Random effects are assumed to be independent and normally distributed. The method of parameter estimation is EM algorithm base on expectation and maximization which falls into the general framework of maximum-likelihood estimations. The performance of the approach was illustrated by data regarding an index of tooth caries on 9-year-old children. Using various dispersion parameters, through Monte Carlo simulations, the multilevel ZIGP yielded more accurate parameter estimates, especially for underdispersed data.

We analyze doubly truncated data using semiparametric transformation models. It is demonstrated that the extended estimating equations of Cheng et al. (1995) can be used to analyze doubly truncated data. The asymptotic properties of the proposed estimators are derived. A simulation study is conducted to investigate the performance of the proposed estimators.

In the usual two-sample scale problem it is assumed that the two populations have a common median. We consider the case where the common quantile may be other than a half. We investigate a quite general class, all members are based on $U$-statistics where the minima and maxima of subsamples of various sizes are used. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen. It is shown that the proposed adaptive test has good asymptotic and finite power properties.

Generalized Type-I and Type-II hybrid censoring schemes as proposed in Chandrasekar et al. (2004) are extended to progressively Type-II censored data. Using the spacings’ based approach due to Cramer and Balakrishnan (2013), we obtain explicit expressions for the density functions of the MLEs. The resulting formulas are given in terms of B-spline functions so that they can be easily and efficiently implemented on a computer.

In competing risks data, missing failure types (causes) is a very common phenomenon. In a general missing pattern, if a failure type is not observed, one observes a set of possible types containing the true type along with the failure time. Dewanji and Sengupta (2003) considered nonparametric estimation of the cause-specific hazard rates and suggested a Nelson–Aalen type estimator under such general missing pattern. In this work, we deal with the regression problem, in which the cause-specific hazard rates may depend on some covariates, and consider estimation of the regression coefficients and the cause-specific baseline hazards under the general missing pattern using some semi-parametric models. We consider two different proportional hazards type semi-parametric models for our analysis. Simulation studies from both the models are carried out to investigate the finite sample properties of the estimators. We also consider an example from an animal experiment to illustrate our methodology.

The purposes of this paper are to introduce a new stochastic order and to study its reliability properties. Some characterizations and preservation properties of the new order under reliability operations of monotone transformation, mixture, weighted distributions and shock models are discussed. In addition, a new class of life distributions is proposed, and some of its reliability properties are investigated. Finally, to illustrate the concepts, some applications in the context of reliability theory and life testing are presented.

We first review the basic properties of Marshall–Olkin bivariate exponential distribution (BVE) and then investigate its correlation structure. We provide the correct reasonings for deriving some properties of the Marshall–Olkin BVE and show that the correlation of the BVE is always smaller than that of its copula regardless of the parameters. The latter implies that the BVE does not have Lancaster’s phenomenon (any nonlinear transformation of variables decreases the correlation in absolute value). The dependence structure of the BVE is also investigated.