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A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution


  • Schlüter, Stephan
  • Fischer, Matthias J.


Calculating a large number of tail probabilities or tail quantiles for a given distribution families becomes very challenging, if both the cumulative and the inverse distribution function are not available in closed form. In case of the Gaussian and Student t distribution, quantile approximations are already available. This is not the case for the (symmetric) generalized hyperbolic distribution (GHD) whose popularity steadily increases and which includes both Gaussian and Student t as limiting case. Within this paper we close this gap and derive one possible tail approximation formula for the GHD as well as for the Student t distribution.

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  • Schlüter, Stephan & Fischer, Matthias J., 2009. "A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution," FAU Discussion Papers in Economics 05/2009, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
  • Handle: RePEc:zbw:iwqwdp:052009

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    1. Jensen, Michael C & Meckling, William H, 1979. "Rights and Production Functions: An Application to Labor-managed Firms and Codetermination," The Journal of Business, University of Chicago Press, vol. 52(4), pages 469-506, October.
    2. John T. Addison & Claus Schnabel & Joachim Wagner, 2004. "The Course of Research into the Economic Consequences of German Works Councils," British Journal of Industrial Relations, London School of Economics, vol. 42(2), pages 255-281, June.
    3. Furubotn, Eirik G, 1988. "Codetermination and the Modern Theory of the Firm: A Property-Rights Analysis," The Journal of Business, University of Chicago Press, vol. 61(2), pages 165-181, April.
    4. Gumbrell-McCormick, Rebecca & Hyman, Richard, 2006. "Embedded collectivism?: workplace representation in France and Germany," LSE Research Online Documents on Economics 750, London School of Economics and Political Science, LSE Library.
    5. Hausman, Jerry A & Taylor, William E, 1981. "Panel Data and Unobservable Individual Effects," Econometrica, Econometric Society, vol. 49(6), pages 1377-1398, November.
    6. Simon Renaud, 2007. "Dynamic Efficiency of Supervisory Board Codetermination in Germany," LABOUR, CEIS, vol. 21(4-5), pages 689-712, December.
    7. Richard B. Freeman & Edward P. Lazear, 1995. "An Economic Analysis of Works Councils," NBER Chapters,in: Works Councils: Consultation, Representation, and Cooperation in Industrial Relations, pages 27-52 National Bureau of Economic Research, Inc.
    8. Felix FitzRoy & Kornelius Kraft, 2005. "Co-determination, Efficiency and Productivity," British Journal of Industrial Relations, London School of Economics, vol. 43(2), pages 233-247, June.
    9. Gérard Charreaux & Philippe Desbrières, 2001. "Corporate Governance: Stakeholder Value Versus Shareholder Value," Journal of Management & Governance, Springer;Accademia Italiana di Economia Aziendale (AIDEA), vol. 5(2), pages 107-128, June.
    10. Luis M. Granero, 2006. "Codetermination, R&D, and Employment," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 162(2), pages 309-328, June.
    11. Kraft Kornelius & Ugarkovič Marija, 2006. "Gesetzliche Mitbestimmung und Kapitalrendite Co-Determination and Return on Equity / Co-Determination and Return on Equity," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 226(5), pages 588-604, October.
    12. Richard Hyman, 1997. "The Future of Employee Representation," British Journal of Industrial Relations, London School of Economics, vol. 35(3), pages 309-336, September.
    13. Barry T. Hirsch, 1991. "Labor Unions and the Economic Performance of Unions," Books from Upjohn Press, W.E. Upjohn Institute for Employment Research, number luepf, November.
    14. Fauver, Larry & Fuerst, Michael E., 2006. "Does good corporate governance include employee representation? Evidence from German corporate boards," Journal of Financial Economics, Elsevier, vol. 82(3), pages 673-710, December.
    15. repec:mes:challe:v:38:y:1995:i:3:p:53-56 is not listed on IDEAS
    16. Barry T. Hirsch, 2004. "What Do Unions Do for Economic Performance?," Journal of Labor Research, Transaction Publishers, vol. 25(3), pages 415-456, July.
    17. FitzRoy, Felix R & Kraft, Kornelius, 1993. " Economic Effects of Codetermination," Scandinavian Journal of Economics, Wiley Blackwell, vol. 95(3), pages 365-375.
    18. Gurdon, Michael A. & Rai, Anoop, 1990. "Codetermination and enterprise performance: Empirical evidence from West Germany," Journal of Economics and Business, Elsevier, vol. 42(4), pages 289-302, November.
    19. Gary Gorton & Frank A. Schmid, 2004. "Capital, Labor, and The Firm: A Study of German Codetermination," Journal of the European Economic Association, MIT Press, vol. 2(5), pages 863-905, September.
    20. Kornelius Kraft & Jörg Stank, 2004. "Die Auswirkungen der gesetzlichen Mitbestimmung auf die Innova-tionsaktivität deutscher Unternehmen," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 124(3), pages 421-449.
    21. Benelli, Giuseppe & Loderer, Claudio & Lys, Thomas, 1987. "Labor Participation in Corporate Policy-Making Decisions: West Germany's Experience with Codetermination," The Journal of Business, University of Chicago Press, vol. 60(4), pages 553-575, October.
    22. Kraft, Kornelius, 2001. "Codetermination as a strategic advantage?," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 543-566, March.
    23. Kraft, Kornelius, 1998. "The codetermined firm in oligopoly," Economics Letters, Elsevier, vol. 61(2), pages 195-201, November.
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    Generalized hyperbolic distribution; Quantile approximation; Student t distribution;

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