Lognormal mean and variance
[M,V] = lognstat(mu,sigma)
[M,V] = lognstat(mu,sigma) returns the mean of and
variance of the lognormal distribution with parameters
sigma are the
mean and standard deviation, respectively, of the associated normal distribution.
sigma can be vectors, matrices, or
multidimensional arrays that all have the same size, which is also the size of
V. A scalar input for
sigma is expanded to a constant array
with the same dimensions as the other input. The parameters in
sigma must be positive.
The normal and lognormal distributions are closely related. If X is distributed lognormally with parameters µ and σ, then log(X) is distributed normally with mean µ and standard deviation σ.
The mean m and variance v of
a lognormal random variable are functions of µ and σ that
can be calculated with the
A lognormal distribution with mean m and variance v has parameters
Generate one million lognormally distributed random numbers with mean 1 and variance 2:
m = 1; v = 2; mu = log((m^2)/sqrt(v+m^2)); sigma = sqrt(log(v/(m^2)+1)); [M,V]= lognstat(mu,sigma) M = 1 V = 2.0000 X = lognrnd(mu,sigma,1,1e6); MX = mean(X) MX = 0.9974 VX = var(X) VX = 1.9776
 Mood, A. M., F. A. Graybill, and D. C. Boes. Introduction to the Theory of Statistics. 3rd ed., New York: McGraw-Hill, 1974. pp. 540–541.