Kontek, Krzysztof (2010): Estimation of Peaked Densities Over the Interval [0,1] Using TwoSided Power Distribution: Application to Lottery Experiments.

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Abstract
This paper deals with estimating peaked densities over the interval [0,1] using twosided 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 twosided 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 twoparametric TP distribution provides more accurate estimates than the smooth threeparametric generalized beta distribution GBT (Libby, Novick, 1982) in one of the considered data sets. The threeparametric 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.
Item Type:  MPRA Paper 

Original Title:  Estimation of Peaked Densities Over the Interval [0,1] Using TwoSided Power Distribution: Application to Lottery Experiments 
Language:  English 
Keywords:  Density Distribution; Maximum Likelihood Estimation; Lottery experiments; Relative Utility Function. 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation ?? C16 ?? C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics C  Mathematical and Quantitative Methods > C9  Design of Experiments > C91  Laboratory, Individual Behavior D  Microeconomics > D0  General > D03  Behavioral Microeconomics: Underlying Principles C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D87  Neuroeconomics 
Item ID:  22378 
Depositing User:  Krzysztof Kontek 
Date Deposited:  29. Apr 2010 00:43 
Last Modified:  13. Feb 2013 07:46 
References:  1. Idzikowska, K., (2009). Determinants of the probability weighting function, presented under name Katarzyna Domurat at SPUSM22 Conference, Rovereto, Italy, August 2009, paper Id = 182, http://discof.unitn.it/spudm22/program_24.jsp . 2. Kontek, K., (2010). Density Based Regression for Inhomogeneous Data; Application to Lottery Experiments, MPRA Paper http://mpra.ub.unimuenchen.de/22268/, Available at SSRN: http://ssrn.com/abstract=1593766 3. Kotz, S., van Dorp, J. R., (2004). Beyond Beta; Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Publishing, Singapore. 4. Libby, D. L., Novick, M. R., (1982). Multivariate generalized beta distributions with applications to utility assessment, Journal of Educational Statistics, 7, pp 271294. 5. Traub, S., Schmidt, U., (2009). An Experimental Investigation of the Disparity between WTA and WTP for Lotteries, Theory & Decision 66 (2009), pp 229262. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/22378 