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Discrete approximations of continuous distributions by maximum entropy

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  • Tanaka, Ken’ichiro
  • Toda, Alexis Akira

Abstract

In numerically implementing the optimization of an expected value in many economic models, it is often necessary to approximate a given continuous probability distribution by a discrete distribution. We propose an approximation method based on the principle of maximum entropy and minimum Kullback–Leibler information, which is computationally very simple. Our method is not intended to replace existing methods but to complement them by “fine-tuning” probabilities so as to match prescribed (not necessarily polynomial) moments exactly.

Suggested Citation

  • Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    • Handle: RePEc:eee:ecolet:v:118:y:2013:i:3:p:445-450
    DOI: 10.1016/j.econlet.2012.12.020
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    References listed on IDEAS

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    1. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
    2. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, December.
    3. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    4. Laura L. Veldkamp, 2011. "Information Choice in Macroeconomics and Finance," Economics Books, Princeton University Press, edition 1, number 9621.
    5. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    6. Alexis Toda, 2010. "Existence of a statistical equilibrium for an economy with endogenous offer sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 379-415, December.
    7. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    8. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
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    Citations

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    Cited by:

    1. Douglas J. Miller & George Judge, 2015. "Information Recovery in a Dynamic Statistical Markov Model," Econometrics, MDPI, vol. 3(2), pages 1-12, March.
    2. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt2tc0m67t, Department of Economics, UC San Diego.
    3. Jianxiong Gao & Zongwen An & Xuezong Bai, 2022. "A new representation method for probability distributions of multimodal and irregular data based on uniform mixture model," Annals of Operations Research, Springer, vol. 311(1), pages 81-97, April.
    4. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    5. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    6. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2017. "No-arbitrage bounds for the forward smile given marginals," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1243-1256, August.
    7. Alexis Akira Toda, 2021. "Data-Based Automatic Discretization of Nonparametric Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1217-1235, April.
    8. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    9. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    10. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    11. Alessandro Barbiero & Asmerilda Hitaj, 2022. "Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models," Annals of Operations Research, Springer, vol. 315(2), pages 1573-1598, August.
    12. Fabrice Tourre, 2017. "A Macro-Finance Approach to Sovereign Debt Spreads and Returns," 2017 Meeting Papers 13, Society for Economic Dynamics.
    13. Jordan Roulleau-Pasdeloup, 2022. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Papers 2209.05081, arXiv.org, revised Feb 2023.
    14. Leland E. Farmer, 2021. "The discretization filter: A simple way to estimate nonlinear state space models," Quantitative Economics, Econometric Society, vol. 12(1), pages 41-76, January.
    15. Alessandro Barbiero & Asmerilda Hitaj, 2023. "Discrete approximations of continuous probability distributions obtained by minimizing Cramér-von Mises-type distances," Statistical Papers, Springer, vol. 64(5), pages 1669-1697, October.

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    More about this item

    Keywords

    Discrete approximation; Fenchel duality; Kullback–Leibler information; Maximum entropy principle;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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