2.1.1.4. LogTriangular Law

If a random variable \(x\) follows a LogTriangular distribution, the random variable \(\ln(x)\) follows a Triangular distribution, so

\[f(x) = \frac{2 \times \ln(x/x_{\rm min})}{ x\times\ln(x_{\rm max}/x_{\rm min}) \times \ln(x_{\rm mode}/x_{\rm min}) } \; {\rm 1\kern-0.28emI}_{[x_{\rm min},x_{\rm mode}]}(x)\]

and

\[f(x) = \frac{2 \times \ln(x_{\rm max}/x)}{ x\times\ln(x_{\rm max}/x_{\rm min}) \times \ln(x_{\rm max}/x_{\rm mode}) } \; {\rm 1\kern-0.28emI}_{[x_{\rm mode},x_{\rm max}]}(x)\]

Figure 2.5 shows the PDF, CDF and inverse CDF generated for different sets of parameters.

Figure 2.5 Example of PDF, CDF and inverse CDF for LogTriangular distributions.