Random chord distributions and containment functions

Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediate...

Distributions of Functions of Normal Random Variables

The unit or standard normal random variable U is a normally distributed variable with mean zero and variance one, i. e. U ∼ N(0, 1). Note that if x ∼ N(µ, σ 2) that x − µ σ ∼ U ∼ N(0, 1) (1) Thus to simulate a normal random variable with mean µ and variance σ 2 , we can simply transform unit normals, as x ∼ µ + σU ∼ N(µ, σ 2) (2) Consider n independent random variables x i ∼ N(µ, σ 2), then x ∼...

Distributions of Functions of Normal Random Variables

Ordered Random Variables from Discontinuous Distributions

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...

Bayesian nonparametric inference for random distributions and related functions

In recent years, Bayesian nonparametric inference, both theoretical and computational, has witnessed considerable advances. However, these advances have not received a full critical and comparative analysis of their scope, impact and limitations in statistical modelling; many aspects of the theory and methods remain a mystery to practitioners and many open questions remain. In this paper, we di...