The ECF-WS estimator for univariate symmetric stable distributions with application in seismic trace signals

Abstract

The parameter that is of most interest in applications of stable distributions is the stability index α, which determines how “heavy” the tail is. For applications when the main interest is on the tail, we develop an estimator of α for univariate symmetric stable distributions, based on the characteristic function and on the principle of wavelet shrinkage. We analyze the proposed estimator by the Monte Carlo simulations and prove that it is a consistent estimator. The presence of human-made explosions in a seismic catalog leads to errors in the statistical analysis of seismicity. Here, we also proposed the CWS coefficient, based on the proposed estimator, like an additional classification tool to discriminate between natural tectonic earthquakes and human-made explosions.

Keywords:

• Earthquakes
• Explosions
• Stable distribution
• Wavelet shrinkage

AMS Classification:

• Primary 60E07
• Secondary 62P12