Mode --- Definition

The Mode is the most likely value of the distribution. It is one of several measures of central tendency, together with the mean and the median. It is the value of x where the probability density function (pdf) of x reaches it's maximum. For a standard normal distribution the mode is at x = 0, the top of the bell-shaped distribution. Not all distribution types have an analytical expression for the mode. Even worse, there may be more than one mode. Where there is no formula for it, iterative procedures heve been invented to approximate the position of the mode.

In the Gaea50 program the mode is estimated by finding the highest density region of the pdf in a list of 20 5% percentile intervals in a vector of 10,000 (sorted) numbers, the result of Monte Carlo modeling. The mean value of x in the shortest interval is the mode estimate. In this interval the distribution function CDF is the steepest, compared to the other percentile intervals.