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).

(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.

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