A unified view on skewed distributions arising from selections

Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main properties of selection distributions and show how various families of multivariate skewed distributions, such as the skew‐normal and skew‐elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.     

二样本问题的假设检验法及其应用

介绍了二样本问题的一种新假设检验方法（SR检验）,SR检验用来探讨如何利用由两连续且相互独立的样本总体中随机抽取的两组独立样本来做假设检验.原理是将二样本差的符号值乘上二样本差加上绝对值后排列的序值（即秩）,取其和为检验统计量,这样就考虑了二样本差的权重以便充分利用收集到的样本所提供的信息比较二样本中位置的关系,并且比较由不同分布的样本总体抽出的样本做出的统计量,用Matlab做模拟比较,提供使用者在非参数统计方法中的另一个选择。     

Measuring sexual partner networks for transmission of sexually transmitted diseases

Patterns of sexual mixing and the sexual partner network are important determinants of the spread of all sexually transmitted diseases (STDs), including the human immunodeficiency virus. Novel statistical problems arise in the analysis and interpretation of studies aimed at measuring patterns of sexual mixing and sexual partner networks. Samples of mixing patterns and network structures derived from randomly sampling individuals are not themselves random samples of measures of partnerships or networks. In addition, the sensitive nature of questions on sexual activity will result in the introduction of non-response biases, which in estimating network structures are likely to be non-ignorable. Adjusting estimates for these biases by using standard statistical approaches is complicated by the complex interactions between the mechanisms generating bias and the non-independent nature of network data. Using a two-step Monte Carlo simulation approach, we have shown that measures of mixing patterns and the network structure that do not account for missing data and non-random sampling are severely biased. Here, we use this approach to adjust raw estimates in data to incorporate these effects. The results suggest that the risk for transmission of STDs in empirical data is underestimated by ignoring missing data and non-random sampling.     

On the Superiority of a Variable Sampling Interval Control Chart

The paper establishes the analytical grounds of the uniform superiority of a variable sampling interval (VSI) Shewhart control chart over the conventional fixed sampling interval (FSI) control chart, with respect to the zero-time performance, for a wide class of process distributions. We provide a sufficient condition on the distribution of a control chart statistic, and propose a criterion to determine the control limits and the regions in the in-control area of the VSI chart, corresponding to the different sampling intervals used by it. The condition and the criterion together ensure the uniform zero-time superiority of the VSI chart over the matched FSI chart, in detecting a process shift of any magnitude. It is shown that normal, Student's t and Laplace distributions satisfy the sufficient condition. In addition, chi-square, F and beta distributions satisfy it, provided that these are not extremely skewed. Further, it is illustrated that the superiority of the VSI feature is not trivial and cannot be assured if the sufficient condition is not satisfied or the control limits and the regions are not determined according to the proposed criterion. An application of the result to confirm the superiority of the VSI feature is demonstrated for the control chart for individual observations used to monitor a milk-pouch filling process.     

Asymptotic expansions relating to discrimination based on two-step monotone missing samples

This paper proposes two asymptotic expansions relating to discrimination based on two-step monotone missing samples. These asymptotic expansions have been obtained by Okamoto (1963) and McLachlan (1973) for complete data under multivariate normality. This paper extends the results up to the terms of the first order in the case of two-step monotone missing samples, respectively. Especially, these asymptotic expansions play important roles in obtaining the asymptotic approximations for the probabilities of misclassification in discriminant analysis. The simulation studies have been also conducted in order to evaluate the accuracy of the approximation derived in this paper.     

Bayesian predictions for compound weibull model

This paper is concerned with a full Bayesian analysis for some prediction problems of the compound model if the underlying distributions are Weibull with unequal shape parameters and the sample is type I censored. A numerical example and computer facilities will be used to illustrate the procedure.     

Confidence limits for stress–strength reliability involving Weibull models

The problem of interval estimation of the stress–strength reliability involving two independent Weibull distributions is considered. An interval estimation procedure based on the generalized variable (GV) approach is given when the shape parameters are unknown and arbitrary. The coverage probabilities of the GV approach are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is very satisfactory even for small samples. For the case of equal shape parameter, it is shown that the generalized confidence limits are exact. Some available asymptotic methods for the case of equal shape parameter are described and their coverage probabilities are evaluated using Monte Carlo simulation. Simulation studies indicate that no asymptotic approach based on the likelihood method is satisfactory even for large samples. Applicability of the GV approach for censored samples is also discussed. The results are illustrated using an example.     

A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples

We establish an independence result concerning a progressive Type-II censored sample from the uniform distribution. This result is used to present a simple and efficient simulational algorithm for generating a progressive Type-II censored sample from any continuous distribution.     

Simplified estimation of the parameters of exponential distribution from samples censored in the middle

This paper presents the small sample optimum choice of k ≤n + r₁ ? r₂ + 1) order statistics for the best linear unbiased estimates (BLUES) of the parameters μ and σ or σ alone ( μ known) when the sample is Type II censored in the middle retaining only r₁ lower and n - r₂ + 1 upper order statistics. For n = 3(1)10, k = 2(1)4, r₁ = O(1) (n?2) and r₂ = (r₁ +2) (l)n, the optimum ranks, the coefficients of the BLUEs have been presented in Table I