Probability Generating Functions for Sattolo’s Algorithm

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. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables. The present article, starting from the de...

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

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...

The IUFP Algorithm for Generating Simulation Heart

In all systems simulation, random variates are considered as a main factor and based of simulation heart. Actually, randomization is inducted by random variates in the simulation. Due to the importance of such a problem, a new method for generation of random variates from continuous distributions is presented in this paper. The proposed algorithm, called uniform fractional part (UFP) is simpler...

Probability Generating Functions for Discrete Real Valued Random Variables

The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random v...