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Flexible statistical models: Methods for the ordering and comparison of theoretical distributions

Robert Rigby, Dimitrios Stasinopoulos and Vlasios Voudouris

MPRA Paper from University Library of Munich, Germany

Abstract: Statistical models usually rely on the assumption that the shape of the distribution is fixed and that it is only the mean and volatility that varies. Although the fitting of heavy tail distributions has become easier due to computational advances, the fitting of the appropriate heavy tail distribution requires knowledge of the properties of the different theoretical distributions. The selection of the appropriate theoretical distribution is not trivial. Therefore, this paper provides methods for the ordering and comparison of continuous distributions by making a threefold contribution. Firstly, it provides an ordering of the heaviness of distribution tails of continuous distributions. The resulting classification of over 30 important distributions is given. Secondly it provides guidance on choosing the appropriate tail for a given variable. As an example, we use the USA box-office revenues, an industry characterised by extreme events affecting the supply schedule of the films, to illustrate how the theoretical distribution could be selected. Finally, since moment based measures may not exist or may be unreliable, the paper uses centile based measures of skewness and kurtosis to compare distributions. The paper therefore makes a substantial methodological contribution towards the development of conditional densities for statistical model in the presence of heavy tails.

Keywords: centile measures; heavy tails; distributions (search for similar items in EconPapers)
JEL-codes: C1 C46 (search for similar items in EconPapers)
Date: 2015-04-13
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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