﻿ Triangular distribution

# 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.

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