A property of coefficients of variation for ordered bivariate log-normal variables

This paper considers the maximum and minimum of a pair of log-normal variables with equal mean. It shows that either order statistic has a smaller coefficient of variation than the two original log-normal variables provided the latter are of equal variance. When the variances are unequal, as the variance ratio increases, the minimum (maximum), has a smaller coefficient of variation if the correlation coefficient of the log-normal variables is small (small) and the variances are large (small).     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.     

Changepoint Estimation in a Segmented Linear Regression via Empirical Likelihood

For a segmented regression system with an unknown changepoint over two domains of a predictor, a new empirical likelihood ratio statistic is proposed to test the null hypothesis of no change. Under the null hypothesis of no change, the proposed test statistic is shown empirically to be Gumbel distributed with robust location and scale estimators against various parameter settings and error distributions. A power analysis is conducted to illustrate the performance of the test. Under the alternative hypothesis with a changepoint, the test statistic is utilized to estimate the changepoint between the two domains. A comparison of the frequency distributions between the proposed estimator and two parametric methods indicates that the proposed method is effective in capturing the true changepoint.     

The Detection of Influential Observations for Allocation,Separation, and the Determination of Probabilities in a Bayesian Framework

Normal theory separation and allocation problems are discussed from a predictive point of view. Influence statistics are defined and employed to ascertain the impact that particular observations will have on the inferential goals—allocation of future observations, separation between populations, and the determination of probabilities for future cases. Methods are illustrated on a collection of financial data taken from Johnson and Wichern (1982).     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.     

Marginal homogeneity,symmetry, and independence

A contingency table of the mc form provides a convenient summary of data when c individuals in a matched set9 each belonging to a different one of c classifications, are identified as belonging to one of m categories, A study in which matched sets (c=3) of 1 case, 1 hospital control, and 1 neighborhood control are classified into one of m=4 occupational categories would be an example, Independence in the cxm tables for each of the matched sets implies symmetry in the summary mc table with consequent marginal homogeneity. Adaptation of the Mantel-Haenszel procedure for testing independence to the case of many cxm tables so as to yield a chi square with (cl)(ml) degrees of freedom (DF) provides a test of marginal homogeneity in the summary mc table. This can be viewed as a test of symmetry directed against alternatives which would make for marginal inhomogeneity and can differ     

Calculation of the expected lifetime lost due to an extra risk

Methods are given for estimating the average years of life lost when a person is discovered to be at risk from an extra hazard. The methods use the probability per year of the extra risk striking, and the mean and standard deviation of lifetime in the absence of the risk. The formulae are simple enough that only a hand‐held calculator is needed.     

白寿彝先生的治学与他的中国通史编纂

白寿彝先生在历史学的许多领域都取得了卓越的成就,晚年主要集中在回族史、中国史学史、中国通史等方面,并表现出总结性、成熟性和继续创新性三个特点。其中中国通史在他的学术规模中居于核心的地位,是他一生研究历史学的最高追求。他带领国内史学家,历20个春秋,终于完成体裁新颖的多卷本中国通史,实现了一个世纪中国史家的愿望,把自己的学术事业推向了辉煌的最高点。     

清代广西三界庙地理分布与三界神信仰探析

三界庙在清代广西各府中都有分布,主要集中分布在南宁、浔州、郁林、平乐、梧州等五府(州),呈现出一种沿着西江流域自东向西递减的分布规律,在郁江两岸分布最为密集。清代广西已经初步形成了三界神祭祀圈,而这种祭祀圈的出现与三界神的现实功利色彩有着密不可分的关系。