A new method of dynamic estimate of seismic danger is presented which is based on estimating multifractal properties of low-frequency seismic noise. The efficiency of the method is illustrated by the analysis of seismic noise from broadband seismic network F-net in Japan. The analysis of...

Using synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions, it is shown that for samples of moderate sizes the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow...

We provide definitive results to close the debate between Eeckhout (2004, 2009) and Levy (2009) on the validity of Zipf’s law, which is the special Pareto law with tail exponent 1, to describe the tail of the distribution of U.S. city sizes. Because the origin of the disagreement between...

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. We develop a battery of new non-parametric and parametric tests to characterize the distributions of empirical returns of...

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge...