Triangular Distribution

probability-theory

Definition

Triangular Distribution

A triangular distribution is a continuous distribution defined on the range $x\in [a,b]$ is parameterised by three parameters:

• $a\in \mathbb{R}$
• $b\in \mathbb{R}\wedge a<b$
• $c\in \mathbb{R}\wedge c\in [a,b]$

¹

Probability Density Function

The probability density function is defined as ¹:

$$P(x)=\{\begin{array}{ll}\frac{2(x-a)}{(b-a)(c-a)}& \text{if}a\le x\le c\\ \frac{2(b-x)}{(b-a)(b-c)}& \text{if}c<x\le b\end{array}$$

Distribution Function

The distribution function is defined as ¹:

$$D(x)=\{\begin{array}{ll}\frac{(x-a{)}^2}{(b-a)(c-a)}& \text{if}a\le x\le c\\ 1-\frac{(b-x{)}^2}{(b-a)(b-c)}& \text{if}c<x\le b\end{array}$$

Footnotes

1. Triangular Distribution — from Wolfram MathWorld ↩ ↩² ↩³