A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one.
- Convex polytope
- Multivariate extreme value distribution
- Pickands dependence function
- Uniform spacings
All Science Journal Classification (ASJC) codes
- Decision Sciences(all)
- Management Science and Operations Research