Random variable xL that is continuously distributed in interval is said to have lognormal distribution described by probability density function fL(xL) if variable xN, that is defined as xN=lnxL, has normal distribution described by probability density function fN(xN) in interval -∞ to ∞.
Denote the mean and variance of normally distributed variable as μ and σ2 respectively, then
mean of XL will be