Properties of the Empirical Distribution Function for Independent Non- Identically Distributed Random Vectors

Translation vectors with non-identically distributed components

A model for non-Gaussian random vectors is presented that relies on a modification of the standard translation transformation which has previously been used to model stationary non-Gaussian processes and non-Gaussian random vectors with identically distributed components. The translation model has the ability to exactly match target marginal distributions and a broad variety of correlation matr...

Generating the Maximum of Independent Identically Distributed Random Variables

Frequently the need arises for the computer generation of variates that are exact/y distributed as 2 = max(X,, . , X.) where X,, . . . , X, form a sequence of independent identically distributed random variables. For large n the individual generation of the Xi’s is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inve...

Distribution of the Maximum of Independent Identically-distributed Variables

Many engineering applications require the calculation of the distribution of the maximum of a number n of indendent, identically distributed (iid) variables. A typical situation is the design of a system for the “n-year demand” when the maximum demands in different years are iid (design of a dam for the n-year flood, design of an offshore platform for the n-year wave, design of a building for t...

Saddlepoint approximations for the sum of independent non-identically distributed binomial random variables

We discuss saddlepoint approximations to the distribution of the sum of independent nonidentically distributed binomial random variables. The saddlepoint solution is the root of a polynomial equation. The paper provides an expression for the coefficients of a polynomial of any degree, the root of which can be found using a simple root-finding algorithm. We examine the accuracy of the saddlepoin...

Distribution of the Maximum of Independent Identically-distributed Variables