This paper addresses the problem of estimating the model parameters of a piecewise multi-linear (PML) approximation to a probability density function (PDF). In an earlier paper, we already introduced the PML model and discussed its use for the purpose of designing Bayesian pattern classifiers. The estimation of the unknown model parameters was based on a least squares minimisation of the difference between the estimated PDF and the estimating PML function. Here, we show how a Maximum Likelihood (ML) approach can be used to estimate the unknown parameters and discuss the advantages of this approach. Subsequently, we briefly introduce its application in a new approach to histogram matching in digital subtraction radiography.