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>