Rigby, Robert and Stasinopoulos, Dimitrios and Voudouris, Vlasios (2015): Flexible statistical models: Methods for the ordering and comparison of theoretical distributions.

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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 boxoffice 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.
Item Type:  MPRA Paper 

Original Title:  Flexible statistical models: Methods for the ordering and comparison of theoretical distributions 
Language:  English 
Keywords:  centile measures, heavy tails, distributions 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics 
Item ID:  63620 
Depositing User:  Dr Vlasios Voudouris 
Date Deposited:  14 Apr 2015 05:11 
Last Modified:  27 Sep 2019 04:30 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/63620 