Dirichlet先验的信息比

通过后验协方差期望的行列式之比研究了作为多项分布参数先验分布的Ｄｉｒｉｃｈｌｅｔ分布的信息性质,导出了Ｄｉｒｉｃｈｌｅｔ分布族及其两个子族及其两个子族的无信息先验分布。     

算术平均值与几何平均值不等式的推广

利用初等对称多项式得出算术平均值与几何平均值不等式的推广形式,并给出[1]中的一个猜想不等式的证明.     

关于一元多项式的除法

着重介绍一种由两个一元多项式的系数变换进行多项式整除性的研究方法 ,在进行多项式整除性的研究时 ,这种方法简单、实用、易懂 ,这种方法还可进一步推广用之于求一元多项式的最大公因式以及一元多项式互素等方面的研究 .     

求解平面静电场的一种方法

提出了一种仅利用初等积分和简单复变函数运算，求解具有一定对称性的平面静电场的方法。     

余弦倍角公式和切比雪夫多项式

在初等数学中,三角函数是一个十分有用的工具．余弦倍角公式是由余弦的幂整系数线性组合来表示倍角的余弦,这样就产生余弦的n倍角能否用余弦的幂次的整系数线性组合表示等问题,通过研究,发现cos nα都是关于2cos α的首项系数为1的、次数等于α的倍数的、系数符号正负相间的整系数多项式,还进一步得到cosnα的一些性质．应用此性质,可以得到一些求和公式及解决许多数学问题．进一步研究,发现此多项式可以转化为切比雪夫多项式,这一多项式及系数有一些有趣的性质．     

交通事故预测方法初探

通过我国城市交通事故采样分析,对国内外流行的几种事故预测方法进行了深入的探讨和辨析,并引出了交通事故预测最佳方法Kalman滤波方法。     

Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics R^a based on power divergence. All R^a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R^a under local alternatives. We obtain an expression of approximation for the distribution of R^a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R^a. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R^a. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.     

淡水渔业的多元多项式回归模型及其应用

本文试图从多元多项式回归模型的特性出发,研究其在渔业技术经济分析中的应用。具体分析了淡水池塘养殖生产中鱼池面积,劳动力与资金投入对总产量的影响程度,并提出了最佳综合养殖措施组合方案和养殖的最佳经营规模。     

A concept of negative dependence using stochastic ordering

A concept of negative dependence called negative dependence by stochastic ordering is introduced. This concept satisfies various closure properties. It is shown that three models for negetive dependence satisfy it and that it implies the basic negative orthant inequalities. This concept is also satisfied by the multinomial, multivariate hypergeometric. Dirichlet and Dirichlet compound multinomial distributions. Furthermore, the joint distribution of ranks of a sample and the multivariate normal with nonpositive pairwise correlations also satisfy this condition. The positive dependence analog of this condition is also studied.     

The Synopsis of the Theory of Pansystems Multinomial Forecasting

The theory of Pansystems Multionomial forecasting (TPMF) is a theory which researches this kind of multinomial forecasting problem:Suppose S(t) is an undnown multinomial, S(j) is the value vector of S(t) at t=t_j. If we get a set of data(S_0, S_1,…, S_n), S_j is an approximate vector of the vector S(j), then how to forecast the vector S(n+1) and what is the maximum of the distance between the forecasting vector and the vector S(n+1) under the condition that S(t) unchanges during the discussion procedure and the range of error is knowm.The purpose of the paper is to give a brief introduction of TPMF.