This study aimed at using a standardized bivariate Pearson family of distribution to generalize a bivariate function and also develop a Parametric Deterministic Model (PDM) that represents mathematical relationship between football matches having trivariate outcomes and the position of teams in the league table. The study established bivariate function as a useful generalization of the univariate Pareto (Type 1) distribution; it also evaluated the previous five-year performance of teams from four major leagues in Europe based on their end of season points(Pik). The Anderson-Darling goodness of fit test (AD-Test) was employed to measure how well the data fits specified theoretical distribution. Negative Binomial distribution is the model that provides the best fit for approximating the distribution of the over-dispersed estimated points associated with six top teams in each of the four leagues. The result revealed Ligue 1 is the most competitive among the four leagues while English Premier League (EPL) is rated the most competitive in the sub-leagues of six teams at the top of the table. The PDM accurately modelled the potential outcomes of series of football matches with the corresponding estimated points for the teams and also generated the league table for EPL using data of 2016/2017 football season.
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