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Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments


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  • Kontek, Krzysztof


This paper deals with estimating peaked densities over the interval [0,1] using two-sided power distribution (Kotz, van Dorp, 2004). Such data were encountered in experiments determining certainty equivalents of lotteries (Kontek, 2010). This paper summarizes the basic properties of the two-sided power distribution (TP) and its generalized form (GTP). The GTP maximum likelihood estimator, a result not derived by Kotz and van Dorp, is presented. The TP and GTP are used to estimate certainty equivalent densities in two data sets from lottery experiments. The obtained results show that even a two-parametric TP distribution provides more accurate estimates than the smooth three-parametric generalized beta distribution GBT (Libby, Novick, 1982) in one of the considered data sets. The three-parametric GTP distribution outperforms GBT for these data. The results are, however, the very opposite for the second data set, in which the data are greatly scattered. The paper demonstrates that the TP and GTP distributions may be extremely useful in estimating peaked densities over the interval [0,1] and in studying the relative utility function.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22378.

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Date of creation: 28 Apr 2010
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Handle: RePEc:pra:mprapa:22378

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Related research

Keywords: Density Distribution; Maximum Likelihood Estimation; Lottery experiments; Relative Utility Function.;

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  1. Schmidt, Ulrich & Traub, Stefan, 2009. "An experimental investigation of the disparity between WTA and WTP for lotteries," Open Access Publications from Kiel Institute for the World Economy, Kiel Institute for the World Economy (IfW) 28786, Kiel Institute for the World Economy (IfW).
  2. Kontek, Krzysztof, 2010. "Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments," MPRA Paper, University Library of Munich, Germany 22268, University Library of Munich, Germany.
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Cited by:
  1. Krzysztof Kontek, 2010. "Maximum likelihood estimator for the uneven power distribution: application to DJI returns," Working Papers, Department of Applied Econometrics, Warsaw School of Economics 43, Department of Applied Econometrics, Warsaw School of Economics.


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