Triangular Distribution - Generating Triangular-distributed Random Variates

Generating Triangular-distributed Random Variates

Given a random variate U drawn from the uniform distribution in the interval (0, 1), then the variate

\begin{matrix} \begin{cases} X = a + \sqrt{U(b-a)(c-a)} & \text{ for } 0 < U < F(c) \\ & \\ X = b - \sqrt{(1-U)(b-a)(b-c)} & \text{ for } F(c) \le U < 1 \end{cases} \end{matrix}

Where F(c) = (c-a)/(b-a)

has a Triangular distribution with parameters a, b and c. This can be obtained from the cumulative distribution function.

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