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An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the integrated Pearson family and the ordinary Pearson system is presented, including an algorithm that enables to decide whether adoi:10.4064/am42-2-9 fatcat:azqdrar7ovhmbamav4fxirv5ii