A probability distribution, usually displayed graphically, shows the relative likelihood of all possible outcomes occurring within a specific time period.

Let F be a probability distribution on R. Then there exist symmetric (about zero) random variables X and Y whose sum has distribution F if and only if F has mean zero or no mean (finite or infinite).

The course covers the probability, distribution theory and statistical inference needed for advanced courses in statistics and econometrics. Michaelmas term: Probability. Conditional probability and ...

In 1959 A. Renyi proposed a set of axioms for a measure of dependence for pairs of random variables. In the same year A. Sklar introduced the general notion of a copula. This is a function which links ...