Examples of Uncorrelated Dependent Random Variables Using a Bivariate Mixture

A particular mixture of bivariate distributions is used to present examples of dependent uncorrelated random variables and independent random variables. A necessary and sufficient condition for the independence for such a bivariate distribution is given.     

Bayesian variable selection with spherically symmetric priors

We propose that Bayesian variable selection for linear parametrizations with Gaussian iid likelihoods should be based on the spherical symmetry of the diagonalized parameter space. Our r-prior results in closed forms for the evidence for four examples, including the hyper-g prior and the Zellner–Siow prior, which are shown to be special cases. Scenarios of a single-variable dispersion parameter and of fixed dispersion are studied, and asymptotic forms comparable to the traditional information criteria are derived. A simulation exercise shows that model comparison based on our r-prior gives good results comparable to or better than current model comparison schemes.     

Dirichlet models for square contingency tables

We consider the square contingency tables which arise when the same method of classification is applied twice. The hypothesis of marginal homogeneity is then relevant! and can be tested by various methods Models are discussed which contain marginal homogeneity as a special case. They include a class based on univariate and bivariate Dirichlet distributions. The question of ordered categories is briefly discussed. Applications are made to data on unaided distance vision.     

On Calculations Involving the Maximum Cell Frequency

We describe a method of computing the cumulative distribution function of the maximum and minimum cell frequencies in sampling distributions commonly encountered in the analysis of categorical data.The procedure is efficient for exact or approximate calculation in both homogeneous and non-homogeneous cases, is non-recursive, and does not require Dirichlet integrals.Some related statistical problems are also discussed.     

Linearity of regression for non-adjacent record values

Let X₁,X₂,… be a sequence of iid random variables having a continuous distribution; by R₁,R₂,… denote the corresponding record values. All the distributions allowing linearity of regressions either E(R_m+k|R_m) or E(R_m|R_m+k) are identified.     

激光散斑相位差的条件统计分布与表面粗糙度的关系

在粗糙表面高度起伏服从高斯统计和表面服从圆型相关的情况下，分析了由弱散射体产生的远场高斯激光散斑相位差的条件统计分布与表面粗糙度的关系．     

AN ANALYTIC FORM FOR THE CUMULATIVE DISTRIBUTION FUNCTION OF THE BELL-DOKSUM STATISTIC

A closed form analytic expression for the Bell-Doksum Statistic is developed. The use of the generalized hypergeometric function to evaluate the expression is demonstrated, and a table of critical values for 2 n 25 is presented.     

Subjective Distributions

A decision maker has to choose one of several random variables whose distributions are not known. As a Bayesian, she behaves as if she knew the distributions. In this paper we suggest an axiomatic derivation of these (subjective) distributions, which is more economical than the derivations by de Finetti or Savage. Whereas the latter derive the whole joint distribution of all the available random variables, our approach derives only the marginal distributions. Correspondingly, the preference questionnaire needed in our case is less smaller.     

Inequality and welfare evaluation of heterogeneous income distributions

This paper establishes the principles that should govern the welfare and inequality analysis of heterogeneous income distributions. Two basic criteria – the equity preference condition and the compensation principle – are shown to be fundamentally incompatible. The paper favours the latter, thereby vindicating the traditional method of dealing with heterogeneous samples. However, inequality and welfare comparisons will usually be well defined only if equivalent incomes are obtained using constant scale factors; and researchers will need to distinguish clearly between inequality of nominal incomes and inequality of living standards. Furthermore, household observations must always be weighted according to family size.     

On influence diagnostic in univariate elliptical linear regression models

We discuss in this paper the assessment of local influence in univariate elliptical linear regression models. This class includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, exponential power and logistic, among others. We derive the appropriate matrices for assessing the local influence on the parameter estimates and on predictions by considering as influence measures the likelihood displacement and a distance based on the Pearson residual. Two examples with real data are given for illustration.