The S-system computation of non-central gamma distribution

The non-central gamma distribution can be regarded as a general form of non-central χ² distributions whose computations were thoroughly investigated (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633; Knüsel, L., 1986, Computation of the chi-square and Poisson distribution. SIAM Journal on Scientific and Statistical Computing, 7, 1022–1036; Voit, E.O. and Rust, P.F., 1987, Noncentral chi-square distributions computed by S-system differential equations. Proceedings of the Statistical Computing Section, ASA, pp. 118–121; Rust, P.F. and Voit, E.O., 1990, Statistical densities, cumulatives, quantiles, and power obtained by S-systems differential equations. Journal of the American Statistical Association, 85, 572–578; Chattamvelli, R., 1994, Another derivation of two algorithms for the noncentral χ² and F distributions. Journal of Statistical Computation and Simulation, 49, 207–214; Johnson, N.J., Kotz, S. and Balakrishnan, N., 1995, Continuous Univariate Distributions, Vol. 2 (2nd edn) (New York: Wiley). Both distributional function forms are usually in terms of weighted infinite series of the central one. The ad hoc approximations to cumulative probabilities of non-central gamma were extended or discussed by Chattamvelli, Knüsel and Bablok (Knüsel, L. and Bablok, B., 1996, Computation of the noncentral gamma distribution. SIAM Journal on Scientific Computing, 17, 1224–1231), and Ruben (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633). However, they did not implement and demonstrate proposed numerical procedures. Approximations to non-central densities and quantiles are not available. In addition, its S-system formulation has not been derived. Here, approximations to cumulative probabilities, density, and quantiles based on the method of Knüsel and Bablok are derived and implemented in R codes. Furthermore, two alternate S-system forms are recast on the basis of techniques of Savageau and Voit (Savageau, M.A. and Voit, E.O., 1987, Recasting nonlinear differential equations as S-systems: A canonical nonlinear form. Mathematical Biosciences, 87, 83–115) as well as Chen (Chen, Z.-Y., 2003, Computing the distribution of the squared sample multiple correlation coefficient with S-Systems. Communications in Statistics—Simulation and Computation, 32(3), 873–898.) and Chen and Chou (Chen, Z.-Y. and Chou, Y.-C., 2000, Computing the noncentral beta distribution with S-system. Computational Statistics and Data Analysis, 33, 343–360.). Statistical densities, cumulative probabilities, quantiles can be evaluated by only one numerical solver power low analysis and simulation (PLAS). With the newly derived S-systems of non-central gamma, the specialized non-central χ² distributions are demonstrated under five cases in the same three situations studied by Rust and Voit. Both numerical values in pairs are almost equal. Based on these, nine cases in three similar situations are designed for demonstration and evaluation. In addition, exact values in finite significant digits are provided for comparison. Demonstrations are conducted by R package and PLAS solver in the same PC system. By doing these, very accurate and consistent numerical results are obtained by three methods in two groups. On the other hand, these three methods are performed competitively with respect to speed of computation. Numerical advantages of S-systems over the ad hoc approximation and related properties are also discussed.     

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Owing to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and non-normality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a large model is inadequate and nothing remains but to consider non- parametric charts. In principle, these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage that seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyse under what conditions non-parametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes that are markedly less huge (but still larger than the customary range). These corrections serve to control the behaviour during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection will clearly be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.     

Bayesian analysis of directed graphs data with applications to social networks

Summary.  A fully Bayesian analysis of directed graphs, with particular emphasis on applica- tions in social networks, is explored. The model is capable of incorporating the effects of covariates, within and between block ties and multiple responses. Inference is straightforward by using software that is based on Markov chain Monte Carlo methods. Examples are provided which highlight the variety of data sets that can be entertained and the ease with which they can be analysed.     

基于政府行政管理职能构建统计体系的基本思路与方法

对某个具体的政府行政职能部门而言,其数据供给和需求常常是不对称的。如何构建一套统计体系,将与其有关的统计数据信息采集、加工、应用、发布通过一个信息系统来实现,以满足其对外的数据供给和对内的数据需求？本文以北京市住建委为例,给出了政府行政职能部门统计体系设计的四个基本步骤：解析行政管理职能,构造统计体系的基本框架,分模块进行具体统计内容设计,落实统计报送周期、数据来源和传输渠道。     

In Memoriam: Emeritus Professor Henry Oliver Lancaster, AO FAA 1 February 1913 – 2 December 2001

The death, in Sydney, of Oliver Lancaster marks the end of an era in the histories of the Statistical Society of Australia, which (in its previous existence as the Statistical Society of New South Wales) he helped found in 1947, and of the Australian Journal of Statistics of which he was founding editor (1959–1971). Oliver Lancaster was Foundation Professor of Mathematical Statistics at the University of Sydney (1959–1978), where he spent his life as student and academic. During his academic career, he achieved scholarly distinction in at least four fields: mathematical statistics, medical and public health statistics, the history of medicine and of statistics, and statistical bibliography. With E.J.G. Pitman (1897–1993), M.H. Belz (1897–1975), E.A. Cornish (1909–1973) and P.A.P. Moran (1917–1988) he was part of a cohort of renowned Australian mathematical statisticians who laid the foundation of the glory days of Australian mathematical statistics. This obituary and tribute focuses on some of these aspects, within a broader historical picture.     

农民专业合作社财务绩效的影响因素分析——基于浙江省319家农民专业合作社的实地调查

基于国内外学者对于农民专业合作社绩效的理论研究成果,本文从合作社运行机制的基本维度、行为（过程）维度和结果维度等三个维度出发,采用农业部为了解全国农民专业合作社各方面情况而专门制作的具有科学性和实用性的问卷,对浙江省319家农民专业合作社进行了实地调查,最后通过应用因子分析和结构方程模型等研究手段探讨了农民专业合作社财务绩效的影响因素。研究结果表明,农民专业合作社的基本情况、经营活动、治理活动和外部环境对财务绩效有显著的正向影响,其中经营活动的影响较大。最后,基于实证结果,提出了进一步推进合作社财务绩效提升的针对性对策建议。     

基于PLS路径模型的顾客满意度测评研究

根据美国顾客满意度指数模型,提出了一种基于PLS路径模型的顾客满意度测评模型;详细阐述了模型设定、模型估计和模型评价。实例证明该顾客满意度测评模型显变量符合单一纬度条件、具有良好的内敛效度、具有一定的解释能力,拟合效果可以接受,为国内顾客满意度测评研究提供了实用方法。     

A Bayesian model for estimating the malaria transition probabilities considering individuals lost to follow-up

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up.     

传统统计面对的挑战

针对统计的黑匣子特性,借用Breiman的两种统计文化的平台,分析传统统计面临的挑战和危机,并探索统计领域究竟要向何处发展的问题。研究表明：统计学必须重新回到针对实际问题而与数据打交道,并且创造有关理论的传统上来。只有这样,才能应对不断产生的新问题所带来的挑战。     

Masking methods that preserve positivity constraints in microdata

Statistical agencies have conflicting obligations to protect confidential information provided by respondents to surveys or censuses and to make data available for research and planning activities. When the microdata themselves are to be released, in order to achieve these conflicting objectives, statistical agencies apply statistical disclosure limitation (SDL) methods to the data, such as noise addition, swapping or microaggregation. Some of these methods do not preserve important structure and constraints in the data, such as positivity of some attributes or inequality constraints between attributes. Failure to preserve constraints is not only problematic in terms of data utility, but also may increase disclosure risk.In this paper, we describe a method for SDL that preserves both positivity of attributes and the mean vector and covariance matrix of the original data. The basis of the method is to apply multiplicative noise with the proper, data-dependent covariance structure.