Approximating the Conway–Maxwell–Poisson distribution normalization constant

By adding a second parameter, Conway and Maxwell created a new distribution for situations where data deviate from the standard Poisson distribution. This new distribution contains a normalization constant expressed as an infinite sum whose summation has no known closed-form expression. Shmueli et al. produced an approximation for this sum but proved that it was valid only for integer values of the second parameter, although they conjectured it was also valid for non-integers. Here we prove their conjecture to be true and discuss for what range of parameters the approximation can be accurately applied.     

Bounds of moment generating functions of some life distributions

In this article we show that if a life has new better than used in expectation (NBUE) ageing property and if the mean life is finite then the moment generating function exists and is finite. In fact, the moment generating function is shown to be bounded above by that of the exponential distribution with the same mean. Analogous results are also proven for two much bigger families of life distribution, namely, the new better than renewal used in expectation (NBRUE) and the renewal new is better than used in expectation (RNBUE) and the renewal new better than renewal used in expectation (RNBRUE), provided that the life has finite two moments. Further, stronger results are also obtained for the smaller new better than used version of the above classes.     

持久冲击与中国经济增长的波动

文章依据一个内在逻辑一致的统计程序考察了1952~2003年间中国实际GDP序列的数据生成过程。发现中国实际GDP序列遵循一个带漂移的随机游走,因而它有一个随机波动的长期趋势;进一步的分析还揭示了长期趋势的波动幅度不小于短期周期性波动的幅度。这些事实在理论上意味着产出序列增长趋势的变化和它经常偏离趋势的运动共同构成了中国产出序列的波动。因此,有理由相信来自供给方面的持久冲击是导致中国经济波动不可忽视的重要原因。     

恒压供水中水泵调速控制的节能分析

阐述了水泵调速控制的节能原理,首先介绍了水泵的节流调节控制流量的方法,然后分析了水泵的转速与各种性能参数的关系,进而研究水泵的调速调节控制流量的方法,将两种控制流量的方法作了对比,分析了调速调节比节流调节节能的原因,最后简要的介绍了变频调速恒压供水系统。     

Detecting multiple change points in piecewise constant hazard functions

The National Cancer Institute (NCI) suggests a sudden reduction in prostate cancer mortality rates, likely due to highly successful treatments and screening methods for early diagnosis. We are interested in understanding the impact of medical breakthroughs, treatments, or interventions, on the survival experience for a population. For this purpose, estimating the underlying hazard function, with possible time change points, would be of substantial interest, as it will provide a general picture of the survival trend and when this trend is disrupted. Increasing attention has been given to testing the assumption of a constant failure rate against a failure rate that changes at a single point in time. We expand the set of alternatives to allow for the consideration of multiple change-points, and propose a model selection algorithm using sequential testing for the piecewise constant hazard model. These methods are data driven and allow us to estimate not only the number of change points in the hazard function but where those changes occur. Such an analysis allows for better understanding of how changing medical practice affects the survival experience for a patient population. We test for change points in prostate cancer mortality rates using the NCI Surveillance, Epidemiology, and End Results dataset.     

An alternative method correcting BDR type of heteroskedasticity by the weighting re-estimated absolute residuals

The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models.     

An optimal k of kth MA-ARIMA models under a class of ARIMA model

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated ARIMA(p, d, q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that 5th exponential weighted moving average (5th EWMA) ARIMA model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study.     

Testing interaction in some predator–prey populations

This paper deals with a testing problem for each of the interaction parameters of the Lotka–Volterra ordinary differential equations system~(ODE). In short, when the rates of birth and death are fixed, we would like to test if each interaction parameter is higher or lower than a fixed reference rate. We choose a statistical model where the actual population sizes are modelled as random perturbations of the solutions to this ODE. By assuming that the random perturbations follow correlated Ornstein–Uhlenbeck processes, we propose the uniformly most powerful test concerning each interaction parameter of the ODE and, we establish the asymptotic properties of the test. Further, we illustrate the suggested test on the Canadian mink–muskrat data set. This research has received the financial support from Natural Sciences and Engineering Research Council of Canada and Institut des Sciences Mathématiques.     

基于主位推进模式的汉英翻译研究

主位推进模式是功能语言学的重要理论,将句子序列作为连贯性的语篇进行研究,是组织语篇信息,实现语言元功能的一种手段.汉英两种语言的主位推进模式有类似和重合之处,定量分析表明二者均可划分为持续型、直线型、独立型和衍生型四种基本模式,但是汉英翻译并非简单地照搬源语的主位推进模式.通过对汉英主位推进模式的对比研究,译者可深入分析话语链中主述位之间的关系,将源语的主位推进模式译为更适合目的语的表达方式,通过语篇的衔接照应等多种方法构建出连贯顺畅的译文.     

Estimation of product moments of a stationary stochastic process with application to estimation of cumulants and cumulant spectral densities

Inference concerning the structure of stationary stochastic processes can be investigated by looking at properties of various cumulant spectral densities of order two and higher. However, except for cases when cumulants and product moments are identical, estimation of higher-order cumulant spectral densities has been restricted by the dependence of higher-order cumulants on lower-order product moments. By first estimating product moments and then using an identity between product moments and cumulants, asymptotically unbiased and consistent estimates of cumulants are obtained. This in turn leads to asymptotically unbiased and consistent estimators of higher-order cumulant spectral densities. In addition, asymptotic normality of product-moment estimators is exhibited under weak dependence.