PROBABILITY GENERATING FUNCTIONS AND THEIR ITERATES

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

Choice probability generating functions

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with speci c properties, and that every function with these speci c properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized b...

Probability Generating Functions

The Growth of Iterates of Multivariate Generating Functions

The vector-valued function m(θ) of a p-vector θ has components m1(θ),m2(θ), . . . ,mp(θ). For each i, exp(mi(−θ)) is the (multivariate) Laplace transform of a discrete measure concentrated on [0,∞)p with only a finite number of atoms. The main objective is to give conditions for the functional iterates m(n) of m to grow like ρn for a suitable ρ > 1. The initial stimulus was provided by results ...

Numerical inversion of probability generating functions

Random quanti t ies of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical t ransform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probability mass functions. However, numerical transform inversion has not been widely used. This lack...