A note on the unimddality of discrete distributions

It is noted that the unimadility property is very inportant and necessary in many probabilistic-statistical models. In this paper, we consider the definition of discrete uniirodality such that the mode may be unique integer or a sequence of consecutive integers. It will be shown that the necessary and sufficient condition for the discrete distribution to be uninnodal about a can be given through some canonical representation of its characteristic function ‘ch.f.’ Further, characterization results for some well-known distributions are established.     

A characterization of a bimodal distribution

As a sequel to Khlnchirie's definition of unimodality a bimodal distribution function is defined, A characterization for such a distribution is given using the well-known result of Khinchine on unimodality and a characterization theorem for a U-shaped probability density function by Ghosh and Shanbhag(1972).     

关于τ（α）函数在概率积分计算中的应用

本文通过τ（α）函数性质及τ（α）函数与B（P,q）函数的关系,得出了τ（α）函数的一系列特殊值,结合概率积分的特点,应用τ（α）函数与B（P,q）函数计算一些概率积分．     

创新不确定条件下溢出效应对企业创新决策影响

合作创新并不总是优于独立创新。在对创新成功的不确定性、技术溢出效应与产品替代性关系讨论的基础上,探讨了在两种创新模式下企业的投入产出水平,确定了两种情况下企业决定进行创新投入时的创新成功概率的最小值,得出结论如下：在技术溢出较小的情况下,产品替代性较低的企业应选择合作创新,产品替代性较高的企业应选择独立创新;在技术溢出较大的情况下,无论产品的替代性如何变化,合作创新对企业更有利。     

关于条件句的蕴涵理论

为了刻画条件句,逻辑学家提出了许多蕴涵理论,如真值函项理论、条件概率理论、信念修正理论、可能世界语义学等。作为现代逻辑的一个分支,条件句逻辑充分利用各种蕴涵思想建立许多逻辑系统,但由于条件句的复杂性,各种蕴涵都难以刻画出所有的条件关系,因此都不能等同于自然语言中的"如果,那么"。     

Cusum quality control-multivariate approach

A new multivariate approach to quality control is presented. On the basis of sequential probability ratio tests, a multivariate cumulative sum chart is derived. Using an approximation to the noncentral x² distribution, a linear decision rule is obtained.     

The exact proability that the roots of quadratic,cubic, and quartic equations are all real if the equation coefficients are random

Suppose that the coefficients of a polynomial equation are Independent random variables defined on subsets of real numbers, The purpose of this paper is to find the exact probability that all roots of a random polynomial equation are real. Since a polynomial equation of degree higher than four with arbitrary coefficients cannot be solved algrebraically, this paper will consider quadratic, cubic and quartic equations only. The general results are obtained in each case, Also, a number of special cases are furnished.     

Discriminating between the generalized Rayleigh and Weibull distributions

Generalized Rayleigh (GR) and Weibull (WE) distributions are used quite effectively for analysing skewed lifetime data. In this paper, we consider the problem of selecting either GR or WE distribution as a more appropriate fitting model for a given data set. We use the ratio of maximized likelihoods (RML) for discriminating between the two distributions. The asymptotic and simulated distributions of the logarithm of the RML are applied to determine the probability of correctly selecting between these two families of distributions. It is examined numerically that the asymptotic results work quite well even for small sample sizes. A real data set involving the annual rainfall recorded at Los Angeles Civic Center during 25 years is analysed to illustrate the procedures developed here.     

三值命题逻辑中公式的概率真度

将三值命题逻辑系统的真度概念引入到概率逻辑,定义公式的期望,给出反映公式之间内在联系的相关系数,研究无限公式收敛时所遵循的规律及特点,引入度量不确定性的特征值—熵.     

The Euclidean distance classifier: an alternative to the linear discriminant function

The sample linear discriminant function (LDF) is known to perform poorly when the number of features p is large relative to the size of the training samples, A simple and rarely applied alternative to the sample LDF is the sample Euclidean distance classifier (EDC). Raudys and Pikelis (1980) have compared the sample LDF with three other discriminant functions, including thesample EDC, when classifying individuals from two spherical normal populations. They have concluded that the sample EDC outperforms the sample LDF when p is large relative to the training sample size. This paper derives conditions for which the two classifiers are equivalent when all parameters are known and employs a Monte Carlo simulation to compare the sample EDC with the sample LDF no only for the spherical normal case but also for several nonspherical parameter configurations. Fo many practical situations, the sample EDC performs as well as or superior to the sample LDF, even for nonspherical covariance configurations.