The probability generating functional

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 probability of generating the symmetric group

In [2], Dixon considered the following question: " Suppose two permutations are chosen at random from the symmetric group Sn of degree n. What is the probability that they will generate Sn? " Actually, Netto conjectured last century that almost all pairs of elements from Sn will generate Sn or An. Dixon showed that this is true in the following sense: The proportion of ordered pairs (x, y) (x, ...

The Probability of Generating a Classical Group

In [KL] it is provcd that the probability of two randomly chosen elements of a finite dassical simple group G actually generating G tends to 1 as lei increases. If gEe, let Pu(g) be the probability that, if h is chosen randomly in G, then (g, h) IG. Let PG : = ma..x{Pu(g) I 9 E e#}. In [KL, Conjecture 2] it is suggested that a stronger result might hold: Pc ---4 0 as IGI ---4 00 for simple clas...