The lognormal distribution (the term first used by Gaddum, 1945) has the probability density function:

where

m |
is the location parameter |

s |
is the scale parameter |

e |
is the base of the natural logarithm, sometimes called Euler's e (2.71...) |

The animation above shows the Log-normal distribution with mu equal to 0 for sigma equals .10, .30, .50, .70, and .90. Note that L represents the critical value from the lognormal distribution displayed in the animation. For a complete listing of all distribution functions, see Distributions and Their Functions.