Showing papers on "Probability-generating function published in 1984"

The Exact-Approximation Method for Generating Random Variables in a Computer

Abstract: A suitably chosen approximation to the inverse of a probability distribution can lead to exact and very fast methods for generating random variables, if the approximation is made exact by adjusting the argument of the approximating function. This article describes the basic method and extensions of it. It gives four examples, of which two are methods for generating gamma- and t-variates that, while meant to illustrate the basic method, show promise of being faster than the best current methods.

An average case analysis of Floyd's algorithm to construct heaps

Abstract: The expected number of interchanges and comparisons in Floyd's well-known algorithm to construct heaps and derive the probability generating functions for these quantities are considered. From these functions the corresponding expected values are computed.

Generating capacity—basic probability methods

Abstract: The determination of the required amount of system generating capacity to ensure an adequate supply is an important aspect of power system planning and operation. The total problem can be divided into two conceptually different areas designated as static and operating capacity requirements. The static capacity area relates to the long-term evaluation of this overall system requirement. The operating capacity area relates to the short-term evaluation of the actual capacity required to meet a given load level. Both these areas must be examined at the planning level in evaluating alternative facilities; however, once the decision has been made, the short-term requirement becomes an operating problem. The assessment of operating capacity reserves is illustrated in Chapter 5.

Method of analysis for discrete-time buffers with randomly interrupted arrival stream

Abstract: The paper considers a discrete buffered system with infinite waiting room, one single output channel and synchronous transmission of messages from the buffer. The arrival stream of messages to the buffer is assumed to be interrupted at random time points for random length time intervals. The arrival interruptions represent a decrease in the mean arrival intensity as compared to a buffer system without arrival interruptions. They also cause the need for a whole new method of analysis, which is presented here. Time is divided into two types of time intervals: `A-times?, during which arrivals are possible, and `B-times?, during which the arrival stream is interrupted. Both types of intervals are expressed in clock time periods and may have arbitrary probability distributions, provided their probability generating functions are rational functions of the variable z. Under these circumstances, expressions are derived for the probability generating functions of the number of messages in the buffer at various time instants. These expressions contain a finite number of unknown parameters, which can only be determined by solving a generally transcendent equation for its roots. As an example of the method, the special case is treated where both A-times and B-times are geometrically distributed; explicit expressions for the probability generating functions of the buffer occupancy are obtained for this special case.

Probabilities and moments of generalized discrete distributfons using finite difference operators

Abstract: The probabilities and factorial moments of the univar iate and multivariate generalized (or compound) discrete di st r-Lbut Lons with probability generating functions H(t)=F(G(t)) and H(t1,…,tk)=F(G(t1,…,tk))or H(t1,…,tk) = F(G1(t1),…, Gk( tk)) are derived using finite difference operators.