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

20 Pages Posted: 1 May 2010

Date Written: April 28, 2010

Abstract

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.

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

JEL Classification: C01, C02, C13, C16, C21, C46, C51, C91, D03, D87

Suggested Citation

Kontek, Krzysztof, Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments (April 28, 2010). Available at SSRN: https://ssrn.com/abstract=1597203 or http://dx.doi.org/10.2139/ssrn.1597203

Krzysztof Kontek (Contact Author)

Warsaw School of Economics (SGH) ( email )

aleja Niepodleglosci 162
PL-Warsaw, 02-554
Poland

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