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The ROOT Mathematical and Statistical libraries have been recently improved both to increase their performance and to facilitate the modelling of parametric functions that can be used for performing maximum likelihood fits to data sets to estimate parameters and their uncertainties. First, we report on the new functionalities introduced in ROOT’s TFormula and TF1 classes to build these models in a convenient way for the users. We show how function objects, represented in ROOT by TF1 classes, can be used as probability density functions and how they can be combined together—via an addition operator—to perform extended likelihood fit of several normalized components. We also describe the new operators introduced to perform the convolution of two functions. Finally, we report on the improvements in the performance of the ROOT fitting algorithm, by using SIMD vectorization when evaluating the model function on large data sets and by exploiting multi-thread parallelization when computing the likelihood function.