2020/04/05 by Nassim Nicholas Taleb, Taleb, Nassim Nicholas
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #Financial Risk and Volatility Modeling #Risk Management (q-fin.RM) #Statistical Distribution Estimation and Applications #Statistical Finance (q-fin.ST) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2004.05894
openalex publication_date 2020/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 α 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 (1)/(n) regardless of the parametrization of the scale and tail index.