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.