TECHNOLOGY OVERVIEW

Log Normal Distribution

BIS.Net Team

A log-normal distribution is a heavily right-skewed distribution of a random independent variable whose logarithm is normally distributed. I.e. If X is log-normal distribution then Y=ln(X) is normally distributed. X can only take positive values. If there are negative values an offset can be added.

If Ln(X) is normally distributed with mean mu and standard deviation sigma then the probability distribution is

Examples of the log-normal distribution can be found in biology, medicine, hydrology, social sciences, reliability and many other. For example the length of a game without time constraints can follow a normal distribution.

Finding the parameters of for a log-normal distribution is straight forward involving calculating the log average and log standard deviation from the sample, as estimators of logmu and log sigma.

Determining the offset is more complicated. BIS.Net Analyst uses a machine powered algorithm to obtain the best estimates of logmu and log sigma and the offset in terms of minimizing the Anderson Darling Statistic