A process capability index with reliable confidence intervals

A well-know process capability index is slightly modified in this article to provide a new measure of process capability which takes account of the process location and variability, and for which point estimator and confidence intervals do exist that are insensitive to departures from the assumption of normal variability. Two examples of applications based on real data are presented.     

A Bivariate Generalization of Gamma Distribution

In this article, a bivariate generalisation of the gamma distribution is proposed by using an unsymmetrical bivariate characteristic function; an extension to the non central case also receives attention. The probability density functions of the product and ratio of the correlated components of this distribution are also derived. The benefits of introducing this generalized bivariate gamma distribution and the distributions of the product and the ratio of its components will be demonstrated by graphical representations of their density functions. An example of this generalized bivariate gamma distribution to rainfall data for two specific districts in the North West province is also given to illustrate the greater versatility of the new distribution.     

Proportional Trapping-Removal Model with a Known Ratio

ABSTRACT

Population size estimator is derived for a proportional trapping-removal model with a known ratio between two sub-population sizes, and the corresponding asymptotic properties is obtained. The performance of the proposed estimator is checked via simulation studies and an example.     

Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper     

A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.     

Normal approximation in an urn model with indistinguishable balls

For the Bose-Einstein Statistics, where n indistinguishable balls are distributed in m urns such that all the arrangements are equally likely, define the random variables

M_k = number of urns containing exactly k balls each;

N_k = number of urns containing at least k balls each.

We consider the approximation of the distributions of M_k and N_k by suitable normal distributions, for large but finite m. Estimates are found for the error in the approximation to both the probability mass function and the distribution function in each case. These results apply also to the alternative model where no urn is allowed to be empty. The results are illustrated by some numerical examples.     

Third-Order Asymptotic Distributions of Classic Test Statistics for One-Parameter Exponential Family Models

ABSTRACT

In this article we derive third-order asymptotic expansions for the non null distribution functions of four classic statistics under a sequence of local alternatives in one-parameter exponential family models. Our results are quite general and cover a wide range of important distributions.     

智性与德性交融工具理性与价值理性统一 --未来道德教育发展的走向

文章通过对中西方道德教育优劣异同的辨析,对当代科技发展所造成的诸多问题的反思,认为未来道德教育必须注重智性与德性的高度完善,科学素质与人文素养的相互融合,工具理性与价值理性的有机统一.     

我国银行保险发展探析

在分析欧洲银行保险迅猛发展的基础上,剖析了起步阶段我国银行保险发展中存在的问题,着重提出了发展我国银行保险的对策:(1)进行保险产品和服务的创新;(2)保险公司信息技术系统的改进与完善;(3)加强银保合作监管。银行保险;银保合作;兼业代理     

汉代关中游侠刍议

两汉时期,关中任侠之气盛行,出现了许多名噪一声的游侠人物。这些游侠一方面拥有打抱不平、行侠仗义、扶危救困的正义精神,在民间享有很高的声誉和威望;另一方面,他们又往往表现出蔑视国法、任意妄为甚至杀人如麻的一面,给国家治安和社会生活造成了很大危害,因而成为官府镇压、屠戮的对象,许多游侠因此结局悲惨。后世文人对于游侠的评价,大多过于看重他们正义、勇武的一面,而对于他们杀人越货、打家劫舍一类的恶行,则往往给予掩饰或美化,不符合历史真实。因此今人在研究过程中应该给游侠以客观、公正、一分为二的评价。