# Accession Number:

## ADA053572

# Title:

## The Distribution of Sums of Dependent Log-Normal Variables.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF MATHEMATICS AND STATISTICS

# Personal Author(s):

# Report Date:

## 1978-04-20

# Pagination or Media Count:

## 32.0

# Abstract:

The present paper studies the properties of the distribution of sums of dependent log-normal random variables and methods to compute numerically their corresponding c.d.f.s. The dependence between the log-normal variables is defined in terms of the correlation between the corresponding normal variables. Two methods for numerical computations of the exact cumulative distributions are developed first. One can be described as a numerical convolution and the other is a Gauss-Legendre quadrature. These methods are compared by numerical results in standard and non-standard cases. The moments of the distribution of the sum are given explicitly and also the coefficients of skewness and kurtosis. It is shown that for positive correlations the distribution of the sum is approximately log-normal. For negative values of the correlation the log-normal becomes ineffective. Another approximation is given for these cases, based on the first few terms of an Edgeworth expansion. Finally, methods for computing the moments of the logarithm of the sum are developed. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability