Another Remark on the Alternative Expectation Formula

Students in a calculus-based probability course will often see the expectation formula for nonnegative continuous random variables in terms of the survival function. This alternative expectation formula has a wide spectrum of applications. It is natural to ask whether there is a multivariate version of this formula. This note gives an affirmative answer by establishing such a formula using two different approaches. The two approaches employed in this note correspond to the two approaches for the univariate case. Supplementary materials for this article are available online.     

Chronic Musculoskeletal Pain:

Two diseases, osteoporosis and osteoarthritis, are responsible for a majority of the chronic musculoskeletal pain that older women experience. Osteoporosis is the metabolic bone disease most common in older women and is responsible for fractures, kyphosis, and chronic pain. Osteoarthritis, the most commonly diagnosed musculoskeletal problem in older women, causes degeneration of the weight-bearing joints in the body, resulting in limited function and chronic pain. In this paper, these and other common disorders are briefly described and typical coping strategies used by older women in pain are reviewed. In addition, potential multidisciplinary treatment regimens are discussed.     

The Importance of Domestic Violence-Sensitive Language

Abstract

It is important for judges to accurately convey what they intend when speaking to litigants involved in domestic violence. Language has idiosyncratic meaning to perpetrators and to victims. Therefore, it is imperative that judges know and understand the language of domestic violence and use it properly. This editorial comments on some of the pitfalls of improper use of language, its impact, and suggests some solutions.     

Participatory community organizing revisited: political involvement and social development in two post-socialist villages in north China

The paper, based on seven months of intensive ethnographic fieldwork in two neighbouring villages in north China, describes a more complicated relationship between members' political involvement and community social development than is generally perceived in literature. The intriguing mechanisms and contents of political participation presented call for a close examination of grassroots political economy, local authority, democratic institutions, and community organizing in the specific social contexts of post-socialist rural China under reforms. The study argues that a context-sensitive understanding of participatory democracy and community development is necessary for the success of macro social work practices, and therefore needs to be built into the curriculum of community organizing and international social work and addressed in social work professional training.     

单指标非参数期权定价——改进的非参数定价方法

本文建立一种改进的非参数期权定价模型,称为单指标非参数期权定价模型。相比现有非参数回归期权定价模型是期权价格关于各个因素的多元回归函数,本模型通过变量变换把期权价格多个因素指标转换为一个综合变量——单指标,得到期权价格关于单指标的一元非参数回归方程。改进的模型实现了多元非参数期权定价模型的降维和简化了模型计算;还通过多个期限期权的单指标组合解决了非参数估计的样本数量问题;以及通过期限平滑解决了现有非参数定价模型中的日历效应问题。选取上证50ETF期权数据实证分析表明,无论是样本内的估计结果还是样本外的预测结果都比传统的Black-Scholes模型、半参数Black-Scholes模型和多元非参数回归期权定价模型估计效果有提高。     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

水性感光胶的理论探讨及发展

本文回顾了水性感光胶的科研开发过程，从设计思路，主要组成及影响感光质量的若干因素等方面作了讨论，重点介绍了重氮盐体系。     

Bayesian semiparametric inference for the accelerated failure-time model

Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data.     

Calibration Estimator of a Rare Sensitive Attribute with Poisson Distribution

In this paper we consider the calibration procedure for a rare sensitive attribute with Poisson distribution which suggested by Land et al. (2012) using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as socio-demographical variables for the respondents of rare sensitive attribute questions from an external source, and then this estimator can be improved with respect to the problems of non coverage or non response. From the efficiency comparison study, we show that the calibrated Poisson RR estimators are more efficient than that of Land et al. (2012), when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.     

On the moment generating functions for integer valued random variables

Abstract

In this note, we give explicit expressions of moment generating functions for integer valued random variables in both univariate and multivariate cases, which extend the results obtained by Nadarajah and Mitov [Communications in Statistics–Theory and Methods, 32, 2003, 47–60] and more recently by Chakraborti, Jardim and Epprecht [The American Statistician, 2017], Kwong and Nadarajah [Communications in Statistics–Theory and Methods, 2017]. Some examples are also discussed.