Transitioning from Discrete to Continuous Distribution Mathematica vs. Excel —An Example  

作　　者：Haiduke Sarafian Haiduke Sarafian(The Pennsylvania State University, University College, York, USA)

机构地区：[1]The Pennsylvania State University, University College, York, USA

出　　处：《American Journal of Computational Mathematics》2022年第1期25-32,共8页美国计算数学期刊（英文）

摘　　要：Frequencies of the repeated integers of the first n digits of e.g. π utilizing commercial software are listed. The discrete distribution is utilized to evaluate its statistical moments. The distribution is fitted with a polynomial generating a continuous replica of the former. Its statistical moments are evaluated and compared to the former. The procedure clarifies the mechanism transiting from discrete to a continuous domain. Applying Mathematica the fitted polynomial is replaced with an interpolated function with controlled smoothing factor refining the quality of the fit and its corresponding moments. Knowledge learned assists in the understanding of the standard procedure calculating moments of e.g. Maxwell-Boltzmann continuous distribution in kinetic Theory of gases.Frequencies of the repeated integers of the first n digits of e.g. π utilizing commercial software are listed. The discrete distribution is utilized to evaluate its statistical moments. The distribution is fitted with a polynomial generating a continuous replica of the former. Its statistical moments are evaluated and compared to the former. The procedure clarifies the mechanism transiting from discrete to a continuous domain. Applying Mathematica the fitted polynomial is replaced with an interpolated function with controlled smoothing factor refining the quality of the fit and its corresponding moments. Knowledge learned assists in the understanding of the standard procedure calculating moments of e.g. Maxwell-Boltzmann continuous distribution in kinetic Theory of gases.

关 键 词：Digits of π Discrete Distribution Continuous Distribution Moments of Distribution EXCEL MATHEMATICA 

分 类 号：O17[理学—数学]