# Comparing Gamma and Log-Normal Distributions

Comparing Gamma and Log-Normal Distributions

This Demonstration compares the gamma distribution and the log-normal distribution . Both of these distributions are widely used for describing positively skewed data. Various distribution plots are shown as well as a table comparing the coefficients of skewness and kurtosis, denoted by and , respectively. Plots of the probability density function (pdf) of the distributions are useful in seeing the overall shape of the distribution but other plots provide additional insights. For example, the plot and normal probability plot are better for showing small differences in the tails.

G

α,β

L

μ,σ

γ

1

γ

2

q-q

Our purpose is to compare the shapes of the gamma and log-normal distributions, so we fix their means to be 1 and constrain their coefficients of variation to be equal. These assumptions require that the log-normal parameter is =log(1+) and that the second gamma parameter is .

2

σ

-1

α

β=

1

α