Q-Pearson Differential Equation With Applications

Abstract

Abstract. The Karl Pearson differential equation stands as a cornerstone in classical statistics, yielding pivotal distributions that underpin  statistical analysis. This paper presents a significant extension of the  Pearson equation, embracing the paradigm of nonextensive statistics and  harnessing the power of the q-logarithm. Through this novel approach,  a family of previously unexplored q-distributions emerges, demonstrating the profound interplay between classical and nonextensive statistical  concepts. The practical implications of these newfound distributions are  highlighted through their application to real-world datasets, which undergo rigorous scrutiny using both the Akaike and small sample Akaike information criteria. This comprehensive analysis underscores the versatility and effectiveness of the proposed framework, fostering a deeper  understanding of statistical behavior across diverse scenarios.