Score Function of Distribution and Heavy-Tails

Authors: Zdeněk Fabián
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of COMPSTAT 2014
Projects: Advanced statistical analysis and non-statistical separation techniques for physical processing detection in data sets sampled by means of elementary particle accelerators.
Bibliographic citation: FABIÁN, Zdeněk. Score Function of Distribution and Heavy-Tails. In: GILLI, M., NIETO-REYES, A., GONZÁLEZ-RODRÍGUEZ, G., eds. Proceedings of COMPSTAT 2014. Geneva: Centre International de Conferences, 2014, S. 657-664. ISBN 978-2-8399-1347-8.
ID: 431044

Abstract

In this contribution we explain the recently introduced notion of the distribution-dependent scalar-valued score function of distribution. Function and its moments are used for description of continuous distributions and data samples generated from them. Each distribution including the heavy-tailed ones and random samples from them are described by a typical value and variability. Further, we discuss the generalized (score) moment estimates and a distribution-dependent score correlation coefficient for continuous random variables, and present results of simulation experiments with data generated from heavy-tailed distributions. Since score functions of distribution of heavy-tailed distributions are bounded, the point estimates as well as the sample score correlation coefficients are insensitive to outliers.