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Approximating the probability distribution of functions of random variables: A new approach

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  • Eric Ghysels
  • Anders Eriksson Lars Forsberg

Abstract

We introduce a new approximation method for the distribution of functions of random variables that are real-valued. The approximation involves moment matching and exploits properties of the class of normal inverse Gaussian distributions. In the paper we we examine the how well the different approximation methods can capture the tail behavior of a function of random variables relative each other. This is obtain done by simulate a number functions of random variables and then investigate the tail behavior for each method. Further we also focus on the regions of unimodality and positive definiteness of the different approximation methods. We show that the new method provides equal or better approximations than Gram-Charlier and Edgeworth expansio

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 503.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:503

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Keywords: Approximation of random variables;

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Cited by:
  1. Javier F. Mencia & Enrique Sentana, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
  2. Puzanova, Natalia & Siddiqui, Sikandar & Trede, Mark, 2009. "Approximate value-at-risk calculation for heterogeneous loan portfolios: Possible enhancements of the Basel II methodology," Journal of Financial Stability, Elsevier, vol. 5(4), pages 374-392, December.
  3. Lillestøl, Jostein, 2007. "Some new bivariate IG and NIG-distributions for modelling covariate nancial returns," Discussion Papers 2007/1, Department of Business and Management Science, Norwegian School of Economics.

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