An infinite series for the computation of the complementary probability distribution function of a sum of independent random variables and its application to the sum of Rayleigh random variables

Author

Beaulieu, Norman C.

Author_Institution

Dept. of Electr. Eng., Queen´´s Univ., Kingston, Ont., Canada

Volume

38

Issue

9

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

1463

Lastpage

1474

Abstract

The properties of the series are studied for both bounded and unbounded random variables. The technique is used to find efficient series for computation of the distributions of sums of uniform random variables and sums of Rayleigh random variables. A useful closed-form expression for the characteristic function of a Rayleigh random variable is presented, and an efficient method for computing a confluent hypergeometric function is given. An infinite series for the probability density function of a sum of independent random variables is also derived. The inversion of characteristic functions, a trapezoidal rule for numerical integration, and the sampling theorem in the frequency domain are related to, and interpreted in terms of, the results

Keywords

information theory; probability; random processes; series (mathematics); signal processing; Rayleigh random variables; bounded random variables; complementary probability distribution function; confluent hypergeometric function; frequency domain; independent random variables; infinite series; numerical integration; sampling theorem; trapezoidal rule; unbounded random variables; Closed-form solution; Distributed computing; Distribution functions; Diversity reception; Fading; Interpolation; Mobile communication; Probability density function; Probability distribution; Random variables;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/26.61387

Filename

61387