A complete computer-based approach for data generation patterning to a pdf in \(\mathbb{R}\) and application to gamma and gig data

Here, we present an automatic data generation method which is fully computer-based for a variate $X$ with an absolutely continuous probability density function (pdf) $f$ exactly computable. The method uses computer-based on calculations of integrals (trapezoidal and/or the Monte-Carlo method) for approximating the cumulative distribution function and next, the dichotomy algorithm to get the quantile function from which we obtain data from \(f\). We apply the method to generate gig(a,b,c) data. The comparison with analogues, as in \textbf{R} Software is very successful. The method may work where the rejection method fails because of a lack of \textit{pdf} bound which can be generated. The method might be slower but the area of more and more powerful computer is favorable to it. The implementation for gamma<\i> and/or gig<\i> laws in R codes are presented.