A review of model selection procedures relevant to the weibull distribution

A number of goodness-of-fit and model selection procedures related to the Weibull distribution are reviewed. These procedures include probability plotting, correlation type goodness-of-fit tests, and chi-square goodness-of-fit tests. Also the Kolmogorow-Smirniv, Kuiper, and Cramer-Von Mises test statistics for completely specified hypothesis based on censored data are reviewed, and these test statistics based on complete samples for the unspecified parameters case are considered. Goodness-of-fit tests based on sample spacings, and a goodness-of-fit test for the Weibull process, is also discussed.

Model selection procedures for selecting between a Weibull and gamma model, a Weibull and lognormal model, and for selecting from among all three models are considered. Also tests of exponential versus Weibull and Weibull versus generalized gamma are mentioned.     

Inverse-gaussian acceptance sampling plans by variables

Variable sampling plans to control fraction defective are obtained using the Inverse-Gaussian (IG) distribution. OC curves are obtained and impact of sample size and specification limits on these curves are discussed. Simulation studies are used to investigate sensitivity of the sampling plans under the more commonly used normal distribution.     

Adaptive estimation of the conditional cumulative distribution function from current status data

Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T  : δ=_I{Y≤T}$\delta ={\mathbb{I}}_{\{Y\le T\}}$ with I$\mathbb{I}$ the indicator function. This paper presents a procedure to estimate the conditional cumulative distribution function F of Y given X   from an independent identically distributed sample of (X,T,δ)$(X,T,\delta )$.     

中国功能性分配格局的国际比较研究

 在当前的研究文献中,我国学者在对中国劳动收入份额进行国际比较时,通常在两个方面产生混乱：一是我国收入法GDP中的劳动者报酬指标包含了非公司业主的混合收入,采用的是宽口径的概念,而SNA1993中的雇员报酬概念却并不包括混合收入,是窄口径的概念。因此,根据我国收入法GDP数据直接计算出的劳动收入份额并不具有国际可比性;二是2004年我国收入法GDP的统计口径本身发生了变动,使得我国2004年前后的劳动收入份额也不具有可比性。本文首先以2004年的经济普查数据为基础,对自我雇佣者的混合收入按照宽、中、窄三种口径进行调整,基本消除了上述的两个不可比因素;其次,以调整后的可比数据为基础,本文对我国宽、中、窄口径的劳动收入份额进行了全面的国际比较,得到的结论更为稳健可靠。结果发现：如果采用窄口径的劳动报酬概念,我国的劳动收入份额不仅低于发达国家的平均水平15～20个百分点,也低于发展中国家的平均水平超过4个百分点。     

基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

Analysis of accelerated life tests with weibull failure distribution via generalized linear models

Efficient industrial experiments for reliability analysis of manufactured goods may consist in subjecting the units to higher stress levels than those of the usual working conditions. This results in the so called "accelerated life tests" where, for each pre-fixed stress level, the experiment ends after the failure of a certain pre-fixed proportion of units or a certain test time is reached. The aim of this paper is to determine estimates of the mean lifetime of the units under usual working conditions from censored failure data obtained under stress conditions. This problem is approached through generalized linear modelling and related inferential techniques, considering a Weibull failure distribution and a log-linear stress-response relationship. The general framework considered has as particular cases, the Inverse Power Law model, the Eyring model, the Arrhenius model and the generalized Eyring model. In order to illustrate the proposed methodology, a numerical example is provided.     

Simulated Distribution of the Kullback-Leibler Information Measure

This paper provides the percentiles obtained by simulation of an informational test statistic. It gives evidence that the widely used chi-square approximation to this test statistic is not suitable.     

High-order extensions of the Double Chain Markov Model

The Double Chain Markov Model is a fully Markovian model for the representation of time-series in random environments. In this article, we show that it can handle transitions of high-order between both a set of observations and a set of hidden states. In order to reduce the number of parameters, each transition matrix can be replaced by a Mixture Transition Distribution model. We provide a complete derivation of the algorithms needed to compute the model. Three applications, the analysis of a sequence of DNA, the song of the wood pewee, and the behavior of young monkeys show that this model is of great interest for the representation of data that can be decomposed into a finite set of patterns.     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.