Statistical Gambler's Ruin Problem

Abstract

The gambler's ruin problem is one of the most important problems in the emergence of probability. The problem has been long considered “solved” from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this paper, the problem is recast as a statistical problem. Bounds of the estimate are derived over wide classes of priors. Interestingly, the probabilistic estimates ω(1/2) are identified as the most conservative solutions while the plug-in estimates are found to be out of range of the bounds. It implies that, although conservative, the probabilistic estimates ω(1/2) are justified by our analysis while the plug-in estimates are too extreme for estimating the ruin probability of gambler.     

A Revised Version of McNemar's Test for Paired Binary Data

In the formula of the McNemar test, a test on 2 × 2 classification tables with pairs of data, only the two categories A and D, which represent changes, are included; the retained parts B and C, which represent concordant responses, are not considered. Generally, it would be more reasonable for the significance of the changes to depend not only on A and D, but also on B and C, or on the sample size, n. To develop the test, two formulae, based on A, D, and n, and on A, D, B, C, and n, respectively, are proposed.     

Testing hypotheses when there could be an initial effect

In many treatment-versus-control experiments, the observed random variables can be written as the product of a Bernoulli and a continuous random variable. The treatment can affect the distribution of the observations in two ways.

1. the probability that the observation is 0 could be altered.

2. the distribution of the nonzero observations could be changed.

We may also want to measure the combined effect of the treatment.

3. the expected value of control and treated units may differ.

A method is presented for testing for the presence of the combined effect when the general form of the distribution function of the continuous observations is known. For the case when this distribution function is from the family of gamma distributions, a previously proposed test criterion for the combined effect has poor power properties. In this paper, we discuss a test criterion that has improved power properties.     

Score tests in the two - way layout of counts

For the balanced two-way layout of a count response variable Y classified by fixed or random factors A and B, we address the problems of (i) testing for individual and interactive effects on Y of two fixed factors, and (ii) testing for the effect of a fixed factor in the presence of a random factor and conversely. In case (i), we assume independent Poisson responses with µ_ij= E(Y| A=i,B=j) = α_iβ_jγ_ij corresponding respectively to the multiplicative

interactive and non-interactive cases. For case (ii) with factor A random, we derive a multivariate gamma-Poisson model by mixing on the random variable associated with each level of A. In each case Neyman C(α) score tests are derived. We present simulation results,and apply the interaction test to a data set, to evaluate and compare the size and power of the score test for interaction between two fixed factors, the competing Poisson-based likelihood ratio test, and the F-tests based on the assumptions that √Y+1 or log(Y+1) are approximately normal. Our results provide strong evidence that the normal-theory based F-tests typically are very far from nominal size, and that the likelihood ratio test is somewhat more liberal than the score test.     

论Charles C.Fries的语料库语言学思想及方法

Charles C.Fries是被语料库语言学界遗忘的一位重量级人物。他既是美国结构主义的代表人物,同时也是一位具有超前意识的语料库语言学思想家和杰出实践者。他的一些语料库语言学思想及方法至今对语料库语言学仍具有指导意义。对其主要的语料库语言学思想及方法:真实客观的数据观、将语言对比特征作为研究的焦点以及实证的研究范式,进行了评述,并在最后指出其思想和方法上的一些缺陷。     

中国农业劳动力转移与农业劳动生产率趋同的实证分析

20世纪90年代以来,中国农业劳动生产率不仅发生了显著的趋同现象,而且已处于向稳态转型的最后阶段;这种趋同是农业产出增长率的变化和因农业劳动力转移而引起的农业就业增长率的变化的相互作用的结果,而且后者的贡献更大;如果仅凭经济系统的自我发展机制,我国区域农业劳动生产率差距终将不会自动消失。必须通过加大投资、进行制度创新、发展乡镇企业和第三产业等措施来人为地缩小区域农业劳动生产率差距,以协调区域经济发展。     

新中国五十年湖南中篇小说巡礼

新中国50年特别是新时期以来的湖南中篇小说,名篇佳构联袂而出,令人目不暇接,文苑震惊,有口皆碑,堪称湖南文学的代表。     

高校化学实验室对环境的污染及其治理

高校化学实验室排放的大量液体、气体、固体废弃物对环境污染严重。认识不到位,投资不足是其产生的主要原因。加强实验室管理,大力推广微型化学实验,推广连续合成实验和回收再利用,分类收集,区别处理是解决问题的主要途径。     

直接碘量法定量测定维生素C

在pH=3的盐酸酸性介质中,碘能定量地将还原型维生素C氧化为脱氢维生素C,淀粉为指示剂,用标准曲线法测定样品中维生素C的含量,从而建立了一种测定维生素C的新方法。该法具有准确度和精密度较高。操作简便,终点变色敏锐,对滴定剂(碘的乙醇溶液)不需要标定等特点。     

Developments in and prospects for external debt position and burden of developing countries: The case of Korea

The delay of strong economic recovery by industrialized nations, slowed world export growth, and higher interest rates have worsened the financial situation of a number of developing countries which have relied on external borrowings to sustain current account deficits and protect economic development. Recently, well-publicized concerns over the ability to these countries to repay their considerable debt burden have been raised. To shed light on these concerns, the paper focuses on Korea—one of the heavier debt-holding countries. It describes the process through which Korea has acquired its external debt over the past decade, assesses the trends in its debt burden, and presents prospects for the period 1982–1986. Using the Korean experience, the paper shows that the most common indicators used for evaluating foreign debt burden, such as the long-term service ratio, need to be supplemented by other measurements. In a world economy characterized by short-term debts with variable interest rates, the paper suggests that an important tool in analyzing the external debt burden should be the short-term debt burden.