This function implements pseudo-random number generation for a doubly non-central \(F\) distribution
$$F=\frac{X_{1}^{2}/n}{X_{2}^{2}/m}$$
where \(X_{1}^{2}\sim \chi^{2}(n,\lambda_{1})\), \(X_{2}^{2}\sim \chi^{2}(m,\lambda_{2})\), \(n\) and \(m\) are numerator and denominator degrees of freedom, respectively, and \(\lambda_{1}\) and \(\lambda_{2}\) are the numerator and denominator non-centrality parameters, respectively. It includes central and singly non-central F distributions as a special case.