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

Krzysztof Kontek ()

No 43, Working Papers from Department of Applied Econometrics, Warsaw School of Economics

Abstract: 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.

Keywords: Density Distribution; Maximum Likelihood Estimation; Stock Returns (search for similar items in EconPapers)
JEL-codes: C01 C02 C13 C16 C46 C87 G10 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2010-05-08
New Economics Papers: this item is included in nep-ecm
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