Moments and generating functions for the absortion distribution and its negative binomial analogue

The moments of the absorption are difficult to obtain. The generating functions are basic hypergeometric functions. This paper shows how to define two shift operators that allow elementary arguments to be used to develop recursions for the expected values of general functions. The exact moments of the distribution follow. The generating function for the negative binomial analogue gives the moments directly.     

Reliability Characteristics of the Maxwell Distribution: A Bayes Estimation Study

ABSTRACT

This article presents maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. A comparison of the relative efficiency of these three estimators is performed via a Monte Carlo simulation study.     

基于Monte Carlo模拟的STAR模型样本矩性质研究

采用Monte Carlo模拟方法对STAR模型样本矩的统计特性进行研究。分析结果表明:STAR模型的样本均值、样本方差、样本偏度及样本峰度都渐近服从正态分布;即使STAR模型的数据生成过程中不含有常数项,其总体均值可能也不是0,这与线性ARMA模型有显著区别;即使STAR模型数据生成过程中的误差项服从正态分布,数据仍有可能是有偏分布。     

Parameter measures of skewness

Several different measures of skewness are commonly used in place of γ₁, the third central moment divided by the cube of the standard deviation. The numerical values of these measures are compared in this paper for members of the gamma, lognormal or Weibull family of distributions and shown to vary considerably in most cases even when skewness and kurtosis are moderate.     

The beta generalized gamma distribution

For the first time, a new five-parameter distribution, called the beta generalized gamma distribution, is introduced and studied. It contains at least 25 special sub-models such as the beta gamma, beta Weibull, beta exponential, generalized gamma (GG), Weibull and gamma distributions and thus could be a better model for analysing positive skewed data. The new density function can be expressed as a linear combination of GG densities. We derive explicit expressions for moments, generating function and other statistical measures. The elements of the expected information matrix are provided. The usefulness of the new model is illustrated by means of a real data set.     

Sociolinguistics and modes of social class signalling: African perspectives

The paper evaluates spatial, behavioural, and material signalling of social class in African contexts, focusing on Kenya and Zambia. In particular, it draws on notions of mode of class signalling and intersectionality and a vignette of an interaction between urban‐based Western educated development agents and local participants in rural Kenya to illustrate how social class is implicated in interactions. The paper shows how significant features of class and dimensions of social inequality may be perceived intersectionally so that positionalities in class structures are negotiated in contexts of interaction, thus illustrating how structural conditions of class may be challenged and questioned. The paper concludes that sociolinguistics needs to identify the various ways in which the marginalized challenge social structures of inequality. Otherwise there is a risk that sociolinguistics will work to validate inequalities as permanent and fixed, and victims of unequal treatment as permanently condemned and never able to rise against oppressive social structures that tyrannize them.     

Estimating mixtures of normal distributions via empirical characteristic function

This paper uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions. Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. It is shown that, using Monte Carlo simulation, the finite sample properties of th ECF estimator are very good, even in the case where the popular maximum likelihood estimator fails to exist. An empirical application is illustrated using the monthl excess return of the Nyse value-weighted index.     

Multigenerational punishments on the children of Salvadoran immigrant and deported fathers

Drawing on qualitative research conducted in the United States and in El Salvador, the author examines the experiences of the children of 40 immigrant men and 40 deported men. This study reveals the harmful effects of U.S. immigration policies and enforcement practices on the children of Salvadoran immigrant and deported fathers. Their children were found to have experienced the unintended consequences of U.S. immigration laws and enforcement practices in their own lives and relationships. These findings support Enriquez's (2015) concept of “multigenerational punishments” where children of immigrant parents share the risks and limitations associated with their parent's immigration status. They also experience the negative spill-over effects of immigration policies and enforcement practices even though they were not directly targeted by these laws. This study reveals multigenerational punishments manifested in the form of social, economic, emotional, and physical inequalities which negatively affected the children of Salvadoran immigrant and deported fathers. As a result, many of their children experienced harmful changes in their lives and relationships under the U.S. immigration enforcement regime. This study is significant in that it provides insight into the issues that immigrant families face and the need for policy interventions for immigrant and deported parents and their children.     

ESTIMATION OF MULTIVARIATE SHANNON ENTROPY USING MOMENTS

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non‐traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment‐recovered approaches with their counterparts derived by using the histogram and k th nearest neighbour constructions. In addition, one worked example is briefly discussed.