Karl Pearson, the founder of mathematical statistics, was the leading statistical researcher from the 1890s up to about 1920. His interests were wide-ranging and so his impact on statistics in the United States was also wide-ranging. Many American researchers came to University College London to...

In his first work on probability, written in 1711, Abraham De Moivre looked at the problem of finding the number of trials required in a binomial experiment to achieve a probability of 1/2 of finding at least some given number of successes. He looked at two cases: when the probability of...

Poisson mixed models are used to analyze a wide variety of cluster count data. These models are commonly developed based on the assumption that the random effects have either the log-normal or the gamma distribution. Obtaining consistent as well as efficient estimates for the parameters involved...

An unbalanced mixed linear model with two variance components is considered, one variance component (say [sigma]12 = 0) corresponding to a random effect (treatments) and a second variance component (say [sigma]2 0) corresponding to the experimental errors. Sufficient conditions are obtained...

We propose a dynamic logistic model for correlated non-stationary longitudinal binary responses collected from many independent individuals. We compute the correlations of the responses under the model and demonstrate that, unlike existing models, full ranges for the correlations are permitted.

It is well known that the ANOVA estimator of the random effects variance component in one-way random effects model can assume negative values. It is also well known that nonnegative quadratic unbiased estimators do not exist for estimating the random effects variance component (LaMotte, 1973)....

The familial-longitudinal data are collected from a large number of groups or families over a small period of time. This type of data exhibit two-way correlations. First, the responses of the members of a family are likely to be correlated. Second, when the familial responses are repeatedly...