Triangular distribution
|
|
Template:Probability distribution
In probability theory and statistics, the triangular distribution is a continuous probability distribution.
<math>f(x|a,b,c)=\left\{
\begin{matrix}
\frac{2(x-a)}{(b-a)(c-a)} & \mathrm{for\ } a \le x \le c \\ & \\
\frac{2(b-x)}{(b-a)(b-c)} & \mathrm{for\ } c < x \le b
\end{matrix}
\right.
<math>
The distribution simplifies when c=a or c=b. For example, if a=0, b=1 and c=1, then the equations above become:
- <math> \left.\begin{matrix}f(x) &=& 2x \\ \\ F(x) &=& x^2 \end{matrix}\right\} \mathrm{for\ } 0 \le x \le 1 <math>
- <math> \begin{matrix}
E(X) &=& \frac{2}{3} \\ & & \\
\mathrm{Var}(X) &=& \frac{1}{18}
\end{matrix} <math>