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We present the underlying relations between colour-magnitude diagrams (CMDs)and synthesis models through the use of stellar luminosity distribution func-tions. CMDs studies make a direct use of the stellar luminosity distributionfunction while, in general, synthesis models only use its mean value, eventhough high-order moments can also be obtained. We show that the mean,high-order moments and in- tegrated luminosity distribution functions ofstellar ensembles are related to the stellar luminosity distribution function,within the formalism of probabilistic synthesis mod- els. More details havebeen yet presented in Cervin ~ o & Luridiana (2006) and references therein. Asa direct application of this formalism, we discuss two key issues. First, in-ferences on the upper mass limit of the initial mass function as a function ofthe total mass of clusters. Second, we apply extreme value theory to show thatthat the cluster mass obtained from normalising the IMF between mmax and mupdoes not provide the cluster mass in the case where only one star in this massrange is present, as assumed in the IGIMF theory. It provides instead thecluster mass with a 60% probability to have a star with mass larger than mmax,and we argue that in light of this result the basic formulation ofthe IGIMFtheory must be revised.

Colour-magnitude diagrams, probabilistic synthesis models and the upper mass limit of the initial mass function