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

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

Contributed by: Diego M. Oviedo Salcedo (April 2017)
(Universidad Pontificia Bolivariana, Bucaramanga, Colombia)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The PDF of a log-normal distribution variable with parameters and is given by

,

where denotes the natural logarithm, and and are related to the variable mean and its standard deviation σ according to

,

.

The PDF for a normal distribution random variable with parameters and is given by

.

,

and similarly, the standard deviation squared, of , is

.

As can be verified using the built-in Mathematica function Expectation, the mean and standard deviation for both the log-normal distribution and normal distribution are and .



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send