Normal and Log-Normal Probability Density Functions with Identical Mean and Standard Deviation

mean

1.2

standard deviation

0.4

normal

log-normal

This Demonstration compares a log-normal distribution probability density function (PDF) with parameters

λ

and

ζ

with a normal distribution PDF with parameters

μ

and

σ

. Both PDFs have identical mean and standard deviation. Since the log-normal distribution is defined for positive values, it is not possible to have an equivalent normal distribution with negative mean.