Working Paper Article Version 3 This version is not peer-reviewed

To Be or to Have Been Lucky, That is the Question

Version 1 : Received: 16 December 2020 / Approved: 17 December 2020 / Online: 17 December 2020 (11:23:32 CET)
Version 2 : Received: 27 December 2020 / Approved: 28 December 2020 / Online: 28 December 2020 (15:31:31 CET)
Version 3 : Received: 19 February 2021 / Approved: 23 February 2021 / Online: 23 February 2021 (15:26:35 CET)

How to cite: lesage, A.; victor, J. To Be or to Have Been Lucky, That is the Question. Preprints 2020, 2020120425 lesage, A.; victor, J. To Be or to Have Been Lucky, That is the Question. Preprints 2020, 2020120425

Abstract

Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

Subject Areas

ex-ante chances; dispersion of chances; maximum entropy principle; chronic diseases; gambling; statistical test; twin studies

Comments (1)

Comment 1
Received: 23 February 2021
Commenter: Jean Marc Victor
Commenter's Conflict of Interests: Author
Comment: Extensively rewritten version with an important new result that is relevant to the field of complex genetic disorders. We here derive the expression of the risk distr ibution to become ill using the maximum entropy principle (see section 4, lines 364-388). We also derive the risk distribution  among affected people, which turns out to have two narrow peaks, one close to p=0 and the other one close to p=1 (see figures 4 and 5 and lines 389-408). The consequences of this functional form are highlighted.
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