2.2.5.8. UniformByParts law

The UniformByParts law is defined between a minimum and a median and between the median and a maximum, as

\[f(x) = \frac{0.5}{(x_{\rm med}-x_{\rm min})} \; {\rm 1\kern-0.28emI}_{[x_{\rm min},x_{\rm med}]}(x) \qquad{\rm and} \qquad f(x) =\frac{0.5}{(x_{\rm max}-x_{\rm med})} \; {\rm 1\kern-0.28emI}_{[x_{\rm med},x_{\rm max}]}(x)\]

Uranie code to simulate a UniformByParts random variable is:

    TDataServer *tds = new TDataServer("tdssampler", "Sampler Uranie demo");
    tds->addAttribute( new TUniformByPartsDistribution("ubp", 0.0, 1.0, 0.5) );
    
    TSampling *fsamp = new TSampling(tds, "lhs", 300);
    fsamp->generateSample(); // Create a representative sample
    
    tds->Draw("ubp");

Figure 2.14 shows the PDF, CDF and inverse CDF generated for different sets of parameters.