Showing papers on "Probability-generating function published in 1973"

The Mean Residual Lifetime Function

Abstract: Necessary and sufficient conditions for a function to be a mean residual lifetime function of a random variable with finite mean are given.

On Characterizing the Extrema of a Function of Two Variables, One of Which is Discrete

Abstract: This research was motivated by design problems in queueing theory where the objective function is composed of a discrete variable and a continuous variable. Sufficient conditions are developed such that any local minimum of such an objective function is also a global minimum. A two-parameter design problem associated with an M/Ek/1 system is used as an example to show how the conditions are utilized.

Two level random number generator having a controllable expected value

Abstract: A random number generator for generating a sequence of binary random numbers (Si) whose expected value is controlled by an input digital number x. The random number generator includes a random bit generator which generates at one output a sequence of mutually independent random variables (RBi) such that the probability P(RBi 0) P(RBi 1) 1/2 . Means are further provided to sequentially analyze the sequence of random variables (RBi) and generate a random variable Li which has a probability function given by P(Li k) 2 k where k 1, 2, 3 . . . each time a pattern of the form (1000 . . . 01) containing (k - 1) zero is detected. Means are further provided to set the output random variable Si of the random number generator equal to the bit Xk of x whenever the random variable Li is equal to k, and this for k 1, 2, 3 . . . .

A recursive method for computing the coefficients of the Gram-Charlier series

Abstract: The Gram-Charlier series is a known tool for approximating a probability density function when the moments or the cumulants of a random variable are known. A recursive procedure is presented which is well suited for the numerical computation of the coefficients of the series.

Random variable generators

Abstract: This note gives APL functions for generating random variables from 21 common statistical distributions:

Nonparametric Bayesian Estimation of Probability Densities by Function Space Techniques

Abstract: : In the study the author considers the problem of estimating the density function which has given rise to a random sample. As opposed to the usual approaches which assume the functional form of the density function a priori, it is assumed that the density function is contained in a broad function class with mild continuity properties. The author then constructs prior measures on the function class and obtain the corresponding posterior measures given the random sample. The function space analogues of the posterior mean and the posterior mode are explored and their consistency properties investigated. Beyond the investigation of appropriate axioms which guarantee the nonparametric implementation of Bayes Theorem, it is shown how to use abstract Wiener measure to give an algorithmic technique for the use of Bayes Theorem in a function space setting. (Modified author abstract)

The Error of a Function Approximation Based on Random Selected Points

Abstract: THE PROBLEM of replacing a complicated function with a simple one — having approximately the same properties often arises both in mathematics and physics. Let us suppose that we have an algorithm for computing the value of the complicated function at any chosen point and we do not have a good estimate about the number and place of points where the value of the complicated function is to be computed in order to get the simple one which may replace it. In this case a random point selection appears advantageous and we give an estimate for the error of the approximation in the cases where this kind of point selection is applied.

Probability estimate of the integration error for IIτ-NETS

Abstract: Πτ-NETS give the best order of convergence of quadratures in the classes of functions Sp. It is proved that for a function chosen at random from Sp the order of convergence is the best possible with an arbitrarily large probability.