Generating autocorrelated pseudo-random numbers with specific distributions

An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.     

The negative contagion reflection of the polya-eggenberger distribution

The Polya-Eggenberger distribution Involves drawing a ball from an urn containing black and white balls and, after each drawing, returning the ball together with s balls of the same color, The model represents positive contagion since the added balls are the same color as the one drawn, See Johnson and Kotz, (1977),

This paper derives and examines the probability distribution which results from the Polya-Eggenberger model with only one change namely, the s additional balls added after each drawing are of the opposite color, producing a negative contagion model.

Formulas in closed form are presented for the probability distribution function, the mean and variance, all binomial moments and, where s is greater than or equal to the number of balls in the urn at start, the mode, A formula for the mode is conjectured where s is less than the number of balls in the urn at start.

Finally, the probability of obtaining k black balls in n drawings is shown in certain instances to be equal to A_nk/n!

where A_nk are the Eulerian numbers.     

Recurrence relations for the minimum variance unbiased estimator of the probability function of the R distribution

We obtain a new technique to calculate the value of the minimum variance unbiased estimator (MVUE) of the probability function (p.f.) of the R distribution. This technique is based on an investigation of the ratios of r numbers. A recurrence relation for the MVUE of the p.f. of the R distribution is derived. It is interesting that the derived relation does not depend on the r numbers but depends on the ratios of the r numbers. The new method is efficient, convenient and accurate.     

Extended stirling family of discrete probability distributions

In this paper. introduced is a family of discrete probability distributions. whose probability function includes explieitly the Striling-Carlitz polynomial of the first or the second kind. The new family extends the stirling family of distributions. Sibuya (1988) includes the conditional distributions of the orginal ones and enlarges the application area.     

王夫之“乾坤并建”的诠释面向——以《周易外传》为中心

乾坤并建是王夫之解易的重要体例,也是他的哲学思想在易学上的鲜明体现。在《周易外传》中,对乾坤并建的诠释集中在以下三个方面:其一,对以邵雍为代表的象数学进行批判,以突出天地的本体地位和对万物的统领作用;其二,对乾坤所代表的知与能、易与简、纯与杂进行阐发,彰显乾与坤在万物的存在与运动中的不同作用:乾给万物以存在及其性质,坤给万物以存在之展开与性质发生功效的能量。乾为健,坤为顺;乾始物,坤成物;万物为杂,乾坤为纯,万物在健与顺的共同作用下产生与运行。其三,太极有易以有于易,代表天地总体的太极就体现在万物之中,太极与万物是体与用的关系,以此拒斥道家的宇宙生成论。     

Weak and strong laws of large numbers for coherent lower previsions

We prove weak and strong laws of large numbers for coherent lower previsions, where the lower prevision of a random variable is given a behavioural interpretation as a subject's supremum acceptable price for buying it. Our laws are a consequence of the rationality criterion of coherence, and they can be proven under assumptions that are surprisingly weak when compared to the standard formulation of the laws in more classical approaches to probability theory.     

免赔额和NCD赔付条件下保险索赔次数的分布

本文分析了免赔额及NCD赔付条件对索赔次数分布的影响,通过比较风险事件与索赔事件的差异引出了一类同质集合保单索赔次数的分布(PG分布);给出了PG分布的性质及参数估计方法。通过两个保险实例展示了数据拟合效果。     

Asymptotic results for empirical and partial-sum processes: A review

Two processes of importance in statistics and probability are the empirical and partial-sum processes. Based on d-dimensional data X₁, … X_a the empirical measure is defined for any A ⊂ R^d by the sample proportion of observations in A. When normalized, F_n yields the empirical process W_n: = n^1/2 (F_n - F), where F denotes the “true” probability measure. To define partial-sum processes, one needs data that are assigned to specified locations (in contrast to the above, where specified unit masses are assigned to random locations). A suitable context for many applications is that of data attached to points of a lattice, say {X_j:j ϵ J^d} where J = {1, 2,…}, for which the partial sums are defined for any A ⊂ R^d by Thus S(A) is the sum of the data contained in A. When normalized, S yields the partial-sum process. This paper provides an overview of asymptotic results for empirical and partial-sum processes, including strong laws and central limit theorems, together with some indications of their inferential implications.     

乘积L—Fuzzy拓扑空间胞腔度的估计

本文就乘积L—Fuzzy拓扑空间的胞腔度,给出了一个适当的上界。     

Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.