Some bivariate uniform distributions

Bivariate uniform distributions with dependent components are readily derived by distribution function transformations of the components of non-uniform dependent continuous bivariate random variables (X,Y). Contour plots of joint density functions show the various, and varying, forms of dependence which can arise from different distributional forms for (X,Y) and aids the choice of bivariate uniform distributions as empirical models.     

A further note on the bivariate normal distribution

It is indicated to what extent the conditional normality of the distribution of one comnonent of a bivariate random vector given the value of the other component together with a restricted type of conditional normality or the marginal normality for the other component is equivalent to the bivariate normality of this random vector.     

On the distribution of rin samples from the mixtures of bivariate normal populations

The distributions of some transformations of the sample correlation coefficient r are studied here, when the parent population is a mixture of two standard bivariate normals. The behavior of these transformations is assessed through the first four standard moments. It is shown that there is a close relationship between the behavior of the transformed variables and the lack of normality as evinced by the 'kurtosis' defined in the bivariate population     

Some inference results on pr(x < y) in the bivariate exponential model

This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.     

Normal quantile estimation based on minimizing the error in predicted distribution functions

Estimators of the form [Xbar] + kS for estimating the p quantile of a normal distribution are studied when k is chosen to either minimize the mean square error in the predicted distribution function or to make the predicted distribution function unbiased for p. Here, [Xbar] and S are the usual sample mean and standard deviation, respectively, and the predicted distribution function is the true (normal) distribution function evaluated at the estimated quantile.

These k values are presented for various sample sizes and values of p, and application to warranty determination is discussed.     

a study of the generalized tukey lambda family

The Tukey lambda family of distributions together with its extensions have played an important role in statistical practice. In this paper a con¬tinuously defined two-parameter generalization of this family, which holds promise of a variety of additional applications, is variously studied. The coefficients of skewness and kurtosis and the density shapes of its members are examined and the family is related to the classical Pearsonian system of distributions.     

Testing for bivariate gumbel against bivariate new better than used in expectation

It is shown that a bivariate survival function is both New Better than Used in Expectation (NBUE) and New Worse than Used in Expectation (NWUE) if and only if it is a bivariate Gumbel distribution. Statistical procedures are then presented to test whether that, within the class of bi-variate NBUE survival functions, a survival function is a Gumbel's bivariate exponential.     

Maximum likelihood estimation of treatment effects for samples subject to cregression to the mean

A general maximum likelihood approach for estimating the effects of treatments applied to samples subject to regression to the mean is outlined. Models may be specified in terms of three factors: whether the treatment effect is multiplicative or additive, whether the treatment group is above or below some truncation point and the type of sample involved. The way in which solutions may be obtained for all 16 models so defined is described.     

Notes on the MLE of correlation coefficient in meta analysis

We study the properties of two approximations to the MLE of the correlation coefficient based on estimates from several studies in meta analysis. Our work is based on an approximation to the density of a function of the sample product-moment estimate due to Dclury, Hsu, and Kraemer. Regarding this approximation, we point out and correct some mistakes in the literature.