Random Number Generator - Log Normal Distribution



 

     
 

The log-normal distribution is often assumed to be the distribution of a stock price.  A distribution is log-normally distributed when the natural log of the set of the random variables in that distribution is a normally distributed.  In plain English, if you take the natural log of each of the random numbers from a log-normal distribution, the new number set will be normally distribution.  Like the normal distribution, log-normal distribtuion is also defined with mean and standard deviation. 

(In Excel, LN( ) is the function that returns the natural log of a number.  EXP( ) is the function that returns e (2.718282) to the power of a given number.  EXP(1)=2.718282, LN(2.718282) = 1.)

The following example shows input and output from 3 simulations.  Each has the same mean (50) with different standard deviation, 5, 10, and 30 respectively.  All three simulations have 50,000 iterations and alpha of 5% (for 1 tail test).


The output shows the estimate of skewness, mean, stand deviation, maximum value, minimum value, lower confidence interval, and upper confidence interval from each of the 3 simulations.  The skewness increases as the standard deviation increases. 

The following shows the charts generated from the 3 simulations.  As the standard deviation increases, the distribution is skewed more to the left.

*Complete program (with open source codes) available in Package Set 2 and the Combo Package.