Maximum Likelihood Estimator for the Uneven Power Distribution: Application to DJI Returns

15 Pages Posted: 2 May 2010 Last revised: 7 May 2010

Date Written: April 30, 2010

Abstract

This paper deals with estimating peaked densities over the interval [0,1] using the Uneven 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 estimations than a smooth distribution. The paper presents the program written in Mathematica which calculates maximum likelihood estimators for all members of the bounded power distribution 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

JEL Classification: C01, C02, C13, C16, C46, C87, G10

Suggested Citation

Kontek, Krzysztof, Maximum Likelihood Estimator for the Uneven Power Distribution: Application to DJI Returns (April 30, 2010). Available at SSRN: https://ssrn.com/abstract=1598438 or http://dx.doi.org/10.2139/ssrn.1598438

Krzysztof Kontek (Contact Author)

Warsaw School of Economics (SGH) ( email )

aleja Niepodleglosci 162
PL-Warsaw, 02-554
Poland

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