On formulas for moments of the Wishart distributions as weighted generating functions of matchings

We consider the real and complex noncentral Wishart distributions. The moments of these distributions are shown to be expressed as weighted generating functions of graphs associated with the Wishart distributions. We give some bijections between sets of graphs related to moments of the real Wishart distribution and the complex noncentral Wishart distribution. By means of the bijections, we see that calculating these moments of a certain class the real Wishart distribution boils down to calculations for the case of complex Wishart distributions. Résumé. Nous considérons les lois Wishart non-centrale réel et complexe. Les moments sont décrits comme fonctions génératrices de graphes associées avex les lois Wishart. Nous donnons bijections entre ensembles de graphes relatifs aux moments des lois Wishart non-centrale réel et complexe. Au moyen de la bijections, nous voyons que le calcul des moments d’une certaine classe la loi Wishart réel deviennent le calcul de moments de loi Wishart complexes.