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Entropy in Nucleus to Tab Data Information and its Illustration with Wolfram Syndrome Cases

Ramalingam Shanmugam

Abstract



A new concept is introduced in this article to tab only pertinent information in the collected data. It is names “entropy in nucleus”. This new concept is versatile, effective, and easier enough to extract data information about an unknown main (that is, incidence) parameter compared to the Shannon’s information. The Shannon information is not always user friendly due to its mathematical and computational difficulties in its practice. The entropy in nucleus has an additive property, which the Shannon’s information does not possess. A secondary (a better name might be accumulation) parameter in a chosen underlying model for the data analysis ought to accumulate the entropies in the observations and it is accomplished in the new approach of entropy in nucleus unlike in the Shannon’s information. Mathematical expressions are developed to obtain the p-value and statistical power for an observed entropy in the nucleus for binomial, Poisson, inverse binomial, exponential, and normal model for a given data. The definitions and derived mathematical expressions for the entropy in nucleus are illustrated using a medical data on the phenotypic symptoms of Wolfram syndrome given in Marshall et al (2013).

Keywords


Artificial intelligence, Kullback-Leibler and Shannon informations, proximity, probability distributions, WFS1 gene, p-value, statistical power.

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