Calculating the mean and variance of power sums with two log-normal components

An efficient method for accurately calculating the mean and variance of power sums with two log-normal components is presented. It involves numerical quadrature with integrands consisting of Gaussian probability density functions. Only the technique of transformation and the trapezoidal rule are used in the evaluation. The whole computational work and roundoff error are much lower than the one by Schwartz and Yeh (1982). Because of its high efficiency, no least-squares fit is necessary. >

[1]  L. Fenton.  The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems , 1960 .

[2]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[3]  J. Naus.  The Distribution of the Logarithm of the Sum of Two Log-Normal Variates , 1969 .

[4]  William A. Janos,et al.  Tail of the distribution of sums of log-normal variates , 1970, IEEE Trans. Inf. Theory.

[5]  M. A. Hamdan.  The Logarithm of the Sum of Two Correlated Log-Normal Variates , 1971 .

[6]  K. S. Kölbig,et al.  Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints , 1972 .

[7]  S. Rice.  Efficient evaluation of integrals of analytic functions by the trapezoidal rule , 1973 .

[8]  D. C. Schleher,et al.  Generalized Gram-Charlier series with application to the sum of log-normal variates (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[9]  S. Schwartz,et al.  On the distribution function and moments of power sums with log-normal components , 1982, The Bell System Technical Journal.

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  Carl W. Helstrom,et al.  Probability and stochastic processes for engineers , 1984 .

[12]  Carl W. Helstrom,et al.  Analysis of avalanche diode receivers by saddlepoint integration , 1992, IEEE Trans. Commun..

[13]  A. Safak,et al.  Statistical analysis of the power sum of multiple correlated log-normal components , 1993 .

[14]  Mehmet Safak,et al.  Moments of the sum of correlated log-normal random variables , 1994, Proceedings of IEEE Vehicular Technology Conference (VTC).

[15]  A. Abu-Dayya,et al.  Outage probabilities in the presence of correlated lognormal interferers , 1994 .