2.2.5.9. Exponential law

This law describes an exponential with a rate parameter \(\lambda\) and a minimum \(x_{\rm min}\), as

\[f(x) = \lambda \times e^{- \lambda \times (x-x_{\rm min})} \; {\rm 1\kern-0.28emI}_{[x_{\rm min},+\infty[}(x)\]

The rate parameter \(\lambda\) should be greater than 0.0001.

Uranie code to simulate an Exponential random variable is:

    TDataServer *tds = new TDataServer("tdssampler", "Sampler Uranie demo");
    tds->addAttribute( new TExponentialDistribution("exp", 0.5));
    
    TSampling *fsamp = new TSampling(tds, "lhs", 300);
    fsamp->generateSample(); // Create a representative sample
    
    tds->Draw("exp");

Figure 2.15 shows the PDF, CDF and inverse CDF generated for different sets of parameters.

../../../_images/TExponentialDistribution.png — Figure 2.15 Example of PDF, CDF and inverse CDF for Exponential distributions.

Is it also possible to set boundaries to the infinite span of this distribution to create a truncated Exponential law. This can be done by calling the following method:

    tds->getAttribute("exp")->setBounds(0.4,6.0); //truncate the law

The resulting PDF, CDF and inverse CDF, with and without truncation, can be seen, in this case, in Figure 2.16 for a given set of parameters and various boundaries.