Limit theorems for dependent Bernoulli variables with statistical inference

We consider a class of dependent Bernoulli variables where the conditional success probability is a linear combination of the last few trials and the original success probability. We obtain its limit theorems including the strong law of large numbers, weak invariance principle, and law of the iterated logarithm. We also derive some statistical inference results which make the model applicable. Simulation results are exhibited as well to show that with small sample size the convergence rate is satisfying and the proposed estimators behave well.     

On the reciprocity of connections in weighted and unweighted networks

Bivariate Bernoulli and bivariate geometric distributions are proposed to model reciprocity in weighted and unweighted networks. Sampling properties of commonly used reciprocity measures are studied, under both presence and absence of reciprocity. Extensions to situations where link parameters depend on outgoing and incoming nodes are investigated. Results are illustrated with a data set, on 50 anesthesia providers at a hospital, that describes the number of times an anesthesia provider starting an operation transfers his/her responsibilities to another anesthesia provider.     

When is n large enough? Looking for the right sample size to estimate proportions

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions.     

Bayesian inference for the parameters of Weibull distribution under progressive Type-I interval censored data with beta-binomial removals

This article considers the problem of estimating the parameters of Weibull distribution under progressive Type-I interval censoring scheme with beta-binomial removals. Classical as well as the Bayesian procedures for the estimation of unknown model parameters have been developed. The Bayes estimators are obtained under SELF and GELF using MCMC technique. The performance of the estimators, has been discussed in terms of their MSEs. Further, expression for the expected number of total failures has been obtained. A real dataset of the survival times for patients with plasma cell myeloma is used to illustrate the suitability of the proposed methodology.     

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables

In this paper, we show that a hypergeometric random variable can be represented as a sum of independent Bernoulli random variables that are, except in degenerate cases, not identically distributed. In the proof, we use the factorial moment generating function. An asymptotic result on the probabilities of the Bernoulli random variables in the sum is also presented. Numerical examples are used to illustrate the results.     

The Guidance Function of Cases of Misappropriation of Public Funds in Transitional China—With the Reference to Criminal Trial of the Supreme People’s Court of China as a Sample of Analysis

相对于贪污、受贿等传统型腐败犯罪, 挪用公款罪不是常态性罪名, 而是针对社 会转型刑法应对的成果。该罪的立法、司法过程中存在着诸多纠结, 这使得判例参考 的价值凸显。最高人民法院十分重视对该罪判例的公布, 这为现实裁决提供了指导和 参考作用。最近10年所公布挪用公款罪判例折射出司法的重心是: 注重主体身份的实 质公务性、从形式合理性理解“归个人使用”、慎重解释“公款”的内涵。判例公布 在有利于同案同判的同时, 也成为促进理论与实践的助推器。

关键词: 腐败犯罪 挪用公款 社会转型 判例 ?刑事审判参考?

Compared with the traditional offenses of embezzlement, bribe-taking and so on, the misappropriation of public funds is not a routine charge but a result of the response of criminal law to social transition. The fact that a number of difficulties have arisen in legislative and judicial procedures relating to this offense makes the value of case reference material significant. The Supreme People’s Court of China attaches great importance to the publication of cases of misappropriation of public funds, which offer guidance and reference for real-life adjudication. Cases publicized in the last decade reflect a judicial emphasis—they focus on the official nature of the duties performed by the subject, on understanding “for individual use” from the viewpoint of formal rationality and on a cautious interpretation of the connotations of “public funds.” Publicizing such cases facilitates reaching the same verdict in similar cases and at the same time acts as a catalyst for the advancement of theory and practice.     

Note on sums of a random number of random variables with exponential family distributions

With the help of the result that exponential-type families are determined by their mean value functions it is shown that stochastic independence of the random variables S_N and N-S_N characterizes the Poisson and Bernoulli distributions simultaneously.     

随机过程的概念解析

通过分析Bernoulli试验对应的随机变量序列,给出随机过程的直观定义导致的矛盾.借助测度论的基本概念系统,解析随机过程的数学定义,给出随机过程样本函数与随机过程实现的概念一致性.     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.