Bivariate Lognormal

Abstract

When two variables are jointly related by the bivariate lognormal distribution, their marginal distributions are lognormal. At first, the distribution appears confounding due to the lognormal characteristics of the variables. By taking the log of each marginal distribution, a pair of normal marginal distributions evolve, and these are jointly related by the bivariate normal distribution described in Chap. 8 (Bivariate Normal). The bivariate normal is defined with the mean and standard deviation of each normal variable and by the correlation between them. These five parameters become the parameters for the counterpart bivariate lognormal distribution. The chapter shows how the mean and variance from the normal is transformed to the mean and variance for the lognormal. Also described is how to compute the correlation of the lognormal from the normal parameters. When sample data is distributed as bivariate lognormal, converting some data and applying the bivariate normal tables of Chap. 8 allow computation for a variety of joint probabilities.