Least Squares Approximations to Lognormal Sum Distributions

Author

Lian Zhao ; Jiu Ding

Author_Institution

Dept. of Electr. & Comput. Eng., Ryerson Univ., Toronto, Ont.

Volume

56

Issue

2

fYear

2007

fDate

3/1/2007 12:00:00 AM

Firstpage

991

Lastpage

997

Abstract

In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RVs). The LS linear approximation is based on the widely accepted assumption that the sum of lognormal RVs can be approximated by a lognormal RV. We further derive the solution for the LS quadratic (LSQ) approximation, and our results show that the LSQ approximation exhibits an excellent match with the simulation results in a wide range of the distributions of the summands. Using the coefficients obtained from the LSQ method, we present the explicit closed-form expressions of the coefficients as a function of the decibel spread and the number of the summands by applying an LS curve fitting technique. Closed-form expressions for the cumulative distribution function and the probability density function for the sum RV, in both the linear and logarithm domains, are presented

Keywords

curve fitting; least squares approximations; log normal distribution; LS quadratic approximation; cumulative distribution function; curve fitting technique; least square linear approximation; lognormal sum distributions; probability density function; Adaptive systems; Closed-form solution; Curve fitting; Distribution functions; Fading; Least squares approximation; Linear approximation; Probability density function; Random variables; Throughput; $L^{2}$-norm; Cumulative distribution functions (CDF); curve fitting; least squares (LS) linear/quadratic approximations; lognormal random variables (RVs); probability density function (pdf);

fLanguage

English

Journal_Title

Vehicular Technology, IEEE Transactions on

Publisher

ieee

ISSN

0018-9545

Type

jour

DOI

10.1109/TVT.2007.891467

Filename

4138061