What You See and What You Don't See: The Hidden Moments of a Probability Distribution

Nassim Nicholas Taleb

Papers from arXiv.org

Abstract: Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order $p$. The method is useful in showing how large a bias one can expect, for a given $n$, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for $\alpha$ close to 1. Among other properties, we note that the "hidden" moment of order $0$, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation $\frac{1}{n}$ regardless of the parametrization of the scale and tail index.

Date: 2020-04
New Economics Papers: this item is included in nep-ecm and nep-rmg
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