Human Lifetime Entropy in a Historical Perspective 1750-2014Report as inadecuate

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1 Lab-STICC TB CID DECIDE Lab-STICC - Laboratoire des sciences et techniques de l-information, de la communication et de la connaissance 2 LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l-Information 3 ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique 4 PSE - Paris-Jourdan Sciences Economiques 5 PSE - Paris School of Economics

Abstract : Although it is widely acknowledged that life is risky, it is difficult to provide an intuitiveindicator of the riskiness of life, whose metric would have a concrete counterpart for the layman.This paper uses the Shannon entropy index to the base 2 to quantify, in terms of bits i.e. the amount of information revealed by tossing a fair coin, the risk relative to the age at death in 37 countries from the Human Mortality Database. We identify 5 major stylized facts: 1 over the last two centuries, period life entropy at birth exhibits an inverted U shape pattern with a maximum in the first half of the 20th century at about 6 bits; 2 over the last 150 years, Western countries have converged in terms of period life entropy at birth towards levels of 5.6 bits for men and 5.5 bits for women; 3 curves of period life entropy at birth for men and women crossed during the 20th century; 4 the entropy age profi le shifted from a non-monotonic profi le in the 18th and 19th centuries to a strictly decreasing pro file in the 20th and 21th centuries; 5 men exhibit a higher life entropy than women below ages 50-55, and a lower one after ages 50-55.

Keywords : mortality risk longevity age at death entropy measurement

Author: Patrick Meyer - Grégory Ponthière -



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