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Maximum likelihood estimator for the uneven power distribution: application to DJI returns

Listed author(s):
  • Krzysztof Kontek


    (Artal Investments, Warsaw)

This paper deals with estimating peaked densities over the interval [0,1] using the Un-even Two-Sided Power Distribution (UTP). This distribution is the most complex of all the bounded power distributions introduced by Kotz and van Dorp (2004). The UTP maximum likelihood estimator, a result not derived by Kotz and van Dorp, is presented. The UTP is used to estimate the daily return densities of the DJI and stocks comprising this index. As the returns are found to have high kurtosis values, the UTP provides much more accurate estima-tions than a smooth distribution. The paper presents the program written in Mathematica which calculates maximum likelihood estimators for all members of the bounded power dis-tribution family. The paper demonstrates that the UTP distribution may be extremely useful in estimating peaked densities over the interval [0,1] and in studying financial data.

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Paper provided by Department of Applied Econometrics, Warsaw School of Economics in its series Working Papers with number 43.

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Length: 15 pages
Date of creation: 08 May 2010
Handle: RePEc:wse:wpaper:43
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  1. Kontek, Krzysztof, 2010. "Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments," MPRA Paper 22378, University Library of Munich, Germany.
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