Contributions to Mathematical Statistics

CONTRIBUTIONS TO ORDER STATISTICS by

Three different problems in order statistics are considered in this dissertation. The first problem deals with the recurrence relations between moments and other functions of order statistics. It is shown that recurrence relations valid for independent and identically distributed random variables continue to hold for exchangeable variables. In the second problem a method, based upon orthogonal ...

Feller's Contributions to Mathematical Biology

This is a review of William Feller’s important contributions to mathematical biology. The seminal paper [Feller 1951] Diffusion processes in genetics was particularly influential on the development of stochastic processes at the interface to evolutionary biology, and interesting ideas in this direction (including a first characterization of what is nowadays known as “Feller’s branching diffusio...

Mathematical biology and medical statistics: contributions to the understanding of AIDS epidemiology.

Some of the many ways in which mathematical biology and statistics have been used in investigating the acquired immunodeficiency syndrome (AIDS) epidemic are reviewed. Aspects of the spread of the disease via social and sexual networks are discussed. The different kinds of data involved are critically compared. Some studies of the incubation period are briefly reviewed and some comments made on...

Mathematical Statistics

This material is designed to introduces basic concepts and fundamental theory of mathematical statistics. A review of basic concepts will include likelihood functions, sufficient statistics, and exponential family of distributions. Then point estimation will be discussed, including minimum variance unbiased estimates, Cramér-Rao inequality, maximum likelihood estimates and asymptotic theory. To...

Mathematical Statistics Old School