Triangular distribution

The triangular distribution (or distribution Simpson, by Thomas Simpson ) is a continuous probability distribution is used in the theory of probability and statistics.

Definition

The distribution is defined by the triangle defined on the interval, probability density function,

The parameters determine ( minimum value), (maximum value), and ( most probable value ) the shape of the triangular distribution. The graph of the density function looks like a triangle, and this distribution is named. The axis shows the density of the respective probability of a value.

Properties

Distribution function

The cumulative distribution function is

The inverse of the cumulative distribution function is

Expected value

The expected value of a triangular distributed random variable is

Variance

The variance of a triangular distributed random variable is given by

Relationship to other distributions

The sum of two identical independent and equally distributed random variables is continuous with a triangular distribution, standard deviation, mean absolute deviation and interquartile range.