多项分布总体的相等对增凸序问题的多样本检验

概率分布间随机序在实践中已经得到了广泛的应用,而且似然比检验是用以检验涉及随机序问题的最普遍的检验方法．但是,关于多个多项式总体间的增凸序约束的统计推断问题并没有得到充分发展．多样本的增凸序对无约束的检验问题已被研究．然而,多总体的相等性对增凸序的假设检验问题似乎更有研究意义．并且分布的相等对随机序的假设检验问题往往是统计学家最为普遍地考虑．对多样本的情况,本文考虑了分布的相等对增凸序的假设检验问题,并且获得似然比检验统计量的零渐近分布,它是一组x~2分布随机变量的加权和,即■~2分布．     

On exponential scores statistics for testing against positive aging

It has been shown in this paper that a test proposed by Barlow and Doksum (1972) based on the exponential scores statistic for testing exponentiality against increasing failure rate distributions is consistent for the much wider class of harmonic new better than used in expectation distributions.     

Bayesian analysis of hybrid life tests with exponential failure times

Summary A hybrid life test procedure is discussed from the Bayesian viewpoint. A total ofn items is placed on test, failed items are either not replaced or are replaced, and the test is terminated either when a pre-chosen number,K, of items have failed, or when a pre-determined time on test has been reached. Posterior and predictive distributions are obtained under the assumption of an exponential failure distribution, and point and interval estimates are given for the mean life and the life of an untested item. The results are applied to a numerical example.     

On the joint distribution of studentized order statistics

In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf's is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936,Biometrika,28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly.     

Testing for increasing convex order in several populations

Increasing convex order is one of important stochastic orderings. It is very often used in queueing theory, reliability, operations research and economics. This paper is devoted to studying the likelihood ratio test for increasing convex order in several populations against an unrestricted alternative. We derive the null asympotic distribution of the likelihood ratio test statistic, which is precisely the chi-bar-squared distribution. The methodology for computing critical values for the test is also discussed. The test is applied to an example involving data for survival time for carcinoma of the oropharynx.     

改进卡方检验

In goodness-of-fit tests, Pearson＇s chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson＇s chi-squared test depends on the partition of the sample space. Different constructions of the partition of the sample space may lead to different conclusions. Based on an equiprobable partition of sample space, a modified chi~quared test is proposed. A method for constructing the modified chi-squared test is proposed. As an application, the proposed test is used to test whether vectorial data come from an uniformity distribution defined on the hypersphere. Some simulation studies show that the modified chisquared test against different alternative is robust.     

Bahadur efficiency and local optimality of a test for exponentiality based on the Moran statistics

We study the scale-free test for exponentiality introduced by Moran. This test has been constructed as an optimal test of exponentiality against the gamma alternatives but it also may be used to test exponentiality against the IFR and DFR classes of alternatives. We obtain rough large deviation asymptotics of the test under the null hypothesis and find its Bahadur efficiency values for most commonly used alternatives to exponentiality. We also describe the local Bahadur optimality domain of the test. The large deviations theorem describes as well the asymptotic behavior of a spacings-based Darling test for uniformity under the null hypothesis. Bibliography: 9 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 245–259.The author is heartily grateful to Prof. Ya. Yu. Nikitin for advices and comments concerning this paper.This research was supported by the Russian Fundation for Basic Research, grant 00-15-96019.Translated by A. V. Tchirina.     

Unit Root Testing in Presence of a Double Threshold Process

In this paper we propose a double threshold process that generalizes the threshold autoregressive one widely known in the literature. It is characterized by a structure with two thresholds: the first regulates the switching between two autoregressive regimes; the second threshold regulates the switching between the two regimes of the stationary innovations. A testing procedure based on a Wald statistic has been given to evaluate the presence of unit roots in the process against stationarity. The asymptotic distribution of the statistic has been derived and the size and the power of the test have been evaluated through a Monte Carlo study where the proposed test is compared to two competing unit root testing procedures. The results clearly highlight the advantage obtained from the proposed test as the asymmetry of the generating process increases.     

BAYESIAN ANALYSIS OF DATA WITH ONLY ONE FAILURE

The hearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of to estimate the reliabilWith a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time, In this paper, we first use hierarchical Bayesian method of determine the prior distribution and the Bayesian estimates of various probabilities of failures, pi‘s, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.     

A Class of Tests on the Tail Index

In the family of distribution functions with nondegenerate right tail, we test the hypothesis with a hypothetical m ₀ > 0 and with some x ₀ 0. The proposed test is fully nonparametric and is based on splitting the set of observations into N subsamples of size n and on the empirical distribution function of the extremes of the subsamples; the asymptotics is for N and fixed n (eventually small), and the asymptotic null distribution of the test criterion is normal. The test is consistent against exponentially tailed alternatives, as well as against heavy tailed alternatives with index m > m ₀, and is asymptotically unbiased for the broad family of distributions represented by and its alternative. It may be used as a supplement to the usual tests of the Gumbel hypothesis m = against m < , namely in the situation that the latter tests reject the hypothesis of exponentiality, and we need to know how heavy-tailed F really can be. This knowledge may be very important in the applications. The performance of the proposed test is illustrated on simulated data; we see that it distinguishes well the tails even for moderate samples. For an illustration, the proposed (nonparametric) test is numerically compared with the (parametric) likelihood ratio test for the class of generalized Pareto distributions. As it can be expected, the parametric test behaves well, provided F is exactly generalized Pareto, while the nonparametric test performs better for all other considered distribution shapes.     

f-Dissimilarity of Several Distributions in Testing Statistical Hypotheses

Various problems in statistics have been treated by the decision rule, based on the concept of distance between distributions. The aim of this paper is to give an approach for testing statistical hypotheses, using a general class of dissimilarity measures among k 2 distributions. The test statistics are obtained by the replacement, in the expression of the dissimilarity measure, of the unknown parameters by their maximum likelihood estimators. The asymptotic distributions of the resulting test statistics are investigated and the results are applied to multinomial and multivariate normal populations.     

均匀分布位置参数的估计量的渐近分布及应用

对区间长度为定值均匀分布位置参数的点估计量进行了研究,得到位置参数点估计量的渐近分布.讨论了渐近分布的相关性质.给出了位置参数的区间估计及其假设检验方法.     

多元Beta分布特性分析

利用小样本截尾序贯检验理论,在武器系统对空中目标的命中精度检验问题中,遇到了一类多元Beta概率分布函数,讨论分析了多维Beta概率分布函数的特性并给出了概率计算表.结果对武器精度检验具有重要意义和实用价值.     

一种寿命试验的费用估算

本文就总体服从指数分布情况，分有替换与无替换定数截尾试验对国外某可靠性标准中一个试验费用公式给出了推导，并对其应用予以讨论。     

Arch model with Box–Cox transformed dependent variable

Box–Cox power transformation has been used traditionally to linearise otherwise nonlinear models. In this paper, Engle's linear ARCH specification is considered for a regression model in which the dependent variable is Box–Cox transformed. The consequent issues arising in both testing and estimation of the model are investigated. A Lagrange multiplier test is also developed to test Engle's linear ARCH model against this wider class of models. The usefulness of this generalisation is examined by applying it to the daily closing prices on the Bombay Stock Exchange Sensitive Index, and the findings strongly favour the proposed model.     

多元正态分布的VDR条件拟合优度检验

提出多元正态性χ2检验统计量.多元正态分布转换样本Yd=RVd服从PearsonII型分布,证明了R2服从贝塔分布.基于贝塔分布和单位球均匀分布,得到多元正态性检验统计量χ2的渐近卡方分布.功效模拟显示,χ2统计量优于已有主要多元正态性检验统计量.做iris数据多元正态性的拟合优度检验.     

基于平稳序列的沪深300股指期货最优套利点研究

基于正态分布和t分布的平稳序列前提,给出了沪深300股指期货跨期套利的最优套利点确定方法.通过对沪深300股指期货不同合约之间的差价进行平稳性检验,发现大部分差价具有平稳性,所以基本适用于给出的最优套利点分析方法.经过对5个平稳差价序列的最优套利点分析,发现△P_(12-07)=IF_(1212)-IF_(1207)和△P_(12-09)=IF_(1212)-IF_(1209)的套利期望收益较大,应该成为沪深300股指期货跨期套利的主要关注对象.     

Testing whether survival function is harmonic new better than used in expectation

Summary Statistical procedures to test that a life distribution is exponential against the alternative that it is harmonic new better than used in expectation (HNBUE) are considered.     

Sensitivity of Bayes decisions for the success probability for samples from a nonbinomial population

Summary A family of generalised negative binomial distributions is employed to investigate inference robustness of the Bayes estimator of the unknown parameter of the binomial distribution. A zone of sensitivity for the test of significance is constructed to forewarn the pro-Jeffreys Bayesians against indiscriminate choice of the probability in favour of the null hypothesis. A few selected tables are presented to illustrate the effect of relaxation of the ‘binomiality’ assumption.     

动力模型参数识别中的Bayes方法

将统计分析中的Bayes方法应用到参数识别问题中,提出了利用测量频率的Bayes估计识别动力学模型的方法,该方法是基于广义逆特征值问题的解。考虑到试验数据的随机性,测量频率用正态分布来描述。此外,将工程师关于测量频率的置信度进行量化,并且与识别过程相结合。数值算例证明了这一方法的有效性。