Quantiles of mixtures with disjoint ordered support

Analytic and Monte Carlo quantiles of a mixture of PDFs with disjoint ordered supports

Unlike the general case, the quantiles of a mixture of PDFs whose supportes are disjoint and ordered can be calculated analytically. This script illustrates the calculation. The example uses a random sample drawn from a single distribution. However, the script is reasonably generic to accommodate an arbitrary number of weights and corresponding PDFs by modifying:

1. an array of weights;
2. an array of tranformations (of the random variable generating the sample)
3. an array of CDF of the random variables resulting from the tranformations.

Furthermore, one could modify the initial sample by changing the either directly or mapping it to another distribution by composition