Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank) = <italic>a</italic> - <italic>b</italic> log(Size), and take <italic>b</italic> as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this...

Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank)=a-b log(Size), and take b as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this...

A popular way to estimate a Pareto exponent is to run an OLS regression: log (Rank) = c - blog (Size), and take b as an estimate of the Pareto exponent. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and argue that, if one...

This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions. We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of...

Let $\xi_1, \ldots, \xi_n$ be independent random variables with ${\bf E}\xi_i=0,$ ${\bf E}|\xi_i|^t<\infty$, $t>2$, $i=1,\ldots, n,$ and let $S_n=\sum_{i=1}^n \xi_i.$ In the present paper we prove that the exact constant ${\overline C}(2m)$ in the Rosenthal inequality $$ {\bf E}|S_n|^t\le C(t) \max...</\infty$,>

We obtain estimates for the best constant in the Rosenthal inequality View the MathML source for independent random variables ξ1,…,ξn with l zero first odd moments, lgreater-or-equal, slanted1. The estimates are sharp in the extremal cases l=1 and l=m, that is, in the cases of random...

This paper studies the properties of the sex ratio in two-period models of threshold (e.g., polygenic or temperature-dependent) sex determination under heavy-tailedness in the framework of possibly skewed stable distributions and their convolutions. We show that if the initial distribution of...

This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio's riskiness if expectations of these risks are infinite. In contrast, for concave...