Lognormal probability density function
Y = lognpdf(X,mu,sigma)
Y = lognpdf(X,mu,sigma) returns
X of the lognormal pdf with distribution
the mean and standard deviation, respectively, of the associated normal
be vectors, matrices, or multidimensional arrays that all have the
same size, which is also the size of
Y. A scalar
expanded to a constant array with the same dimensions as the other
The lognormal pdf is
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
So, a lognormal distribution with mean m and variance v has parameters
If you do not know the population mean and variance, m and v, for the lognormal distribution, you can estimate and in the following way:
mu = mean(log(X)) sigma = std(log(X))
The lognormal distribution is applicable when the quantity of interest must be positive, since log(X) exists only when X is positive.
Compute the pdf of a lognormal distribution with
mu = 0 and
sigma = 1.
x = (0:0.02:10); y = lognpdf(x,0,1);
Plot the pdf.
plot(x,y); grid; xlabel('x'); ylabel('p')
 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.