On the Super-Additivity and Estimation Biases of Quantile Contributions

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On the Super-Additivity and Estimation Biases of Quantile Contributions

Nassim N Taleb, Raphael Douady
(Submitted on 8 May 2014 (v1), last revised 12 Nov 2014 (this version, v3))
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.

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Those who are attempting to turn Jihadi John into “a victim” are, simply, his collaborators…

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by default 2015-02-27 at 12.31.42 PM

Those who are attempting to turn Jihadi John into “a victim” are, simply, his collaborators/promoters and need to be treated as such.

via Nassim NicholنTaleb on Twitter: “Those who are attempting to turn Jihadi John into “a victim” are, simply, his collaborators/promoters and need to be treated as such.”.

The absolute best best best noBS book on hist of probability is Franklin’s

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NNT tweeted: “The absolute best best best noBS book on hist of probability is Franklin’s” and linked to his Amazon review.
5.0 out of 5 stars Indispensable, August 31, 2013

By N N Taleb

This review is from: The Science of Conjecture: Evidence and Probability before Pascal (Paperback)

As a practitioner of probability, I’ve read many book on the subject. Most are linear combinations of other books and ideas rehashed without real understanding that the idea of probability harks back the Greek pisteuo (credibility) [and pithanon that led to probabile in latin] and pervaded classical thought. Almost all of these writers made the mistake to think that the ancients were not into probability. And most books such “Against the Gods” are not even wrong about the notion of probability: odds on coin flips are a mere footnote. If the ancients were not into computable probabilities, it was not because of theology, but because they were not into games. They dealt with complex decisions, not merely probability. And they were very sophisticated at it.

This book stands above, way above the rest: I’ve never seen a deeper exposition of the subject, as this text covers, in addition to the mathematical bases, the true philosophical origin of the notion of probability. In addition Franklin covers matters related to ethics and contract law, such as the works of the medieval thinker Pierre de Jean Olivi, that very few people discuss today.

via Amazon.com: N N Taleb “Nassim Nicholas Taleb”‘s review of The Science of Conjecture: Evidence and Pr….