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

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

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.

• Item Type: MPRA Paper
• 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; ; 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 - Cross-Sectional 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

References

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