TITLE:
Transitioning from Discrete to Continuous Distribution Mathematica vs. Excel —An Example
AUTHORS:
Haiduke Sarafian
KEYWORDS:
Digits of π, Discrete Distribution, Continuous Distribution, Moments of Distribution, Excel, Mathematica
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.12 No.1,
March
8,
2022
ABSTRACT: 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.