Probability-generating function

About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.

Generation of random sequences with jointly specified probability density and autocorrelation functions

Abstract: A new method is presented for the generation of stochastic (random) sequences with an arbitrarily specified first-order probability distribution function (PDF) and an arbitrarily specified first-roder auto-correlation function (ACF). A set of numbers with the desired PDF are first generated. These are then given a white (independent) ACF by double stochastic interchange. The desired ACF is then obtained by stochastically shuffling the series to minimize a sum of squares criterion between desired and actual ACFs. The technique is particularily useful for generating experimental stimuli for system identification, sequences for numerical simulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.

Synthesizing Nonstationary, Non-Gaussian Random Vibrations

Abstract: This paper presents a novel technique by which non-Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root mean square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non-Gaussian vibrations can be decomposed into a sequence of Gaussian processes. Synthesis is achieved by first computing a modulation function which is produced from the rms and the segment length distribution functions, both of which were developed in previous research. This is achieved by first generating a sequence of uniformly distributed random numbers scaled to the range of segment length, which itself is a function of the desired total duration of the synthesized process. In order to transform a uniformly distributed random variable into any arbitrary non-uniform distribution, the cumulative distribution function is established and used as a transfer function applied to the uniformly distributed random variable. This modulation function is applied to a Gaussian random signal itself generated by a standard laboratory random vibration controller (RVC) by means of a purposed-designed variable gain amplifier system. In order to counteract the feedback function of the RVC, a second variable gain amplifier is introduced into the system in order to attenuate the feedback signal in inverse proportion to the gain applied to the command signal. This result is a nonstationary, non-Gaussian random signal that statistically conforms to the desired PSD as well as the RMS distribution function. Copyright © 2010 John Wiley & Sons, Ltd.

Sum of Weibull variates and performance of diversity systems

Abstract: Sum of Weibull random variables (RVs) is naturally of prime importance in wireless communications and related areas. Through the medium of the selection of poles as orthogonal Laguerre polynomials in Cauchy residue theorem, the moment-generation function (MGF), the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of L ≥ 2 mutually independent any random variables (RVs) are represented in terms of fast convergent series, and the obtained results are applied to the sum of Weibull RVs in order to find symbol error rate (SER) and outage probability (OP) performance.

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.