IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v118y2013i3p445-450.html
   My bibliography  Save this article

Discrete approximations of continuous distributions by maximum entropy

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176512006568
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2012.12.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    3. 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.
    4. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    5. Laura L. Veldkamp, 2011. "Information Choice in Macroeconomics and Finance," Economics Books, Princeton University Press, edition 1, number 9621.
    6. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    7. 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.
    8. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roulleau-Pasdeloup, Jordan, 2023. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    2. 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.
    3. Douglas J. Miller & George Judge, 2015. "Information Recovery in a Dynamic Statistical Markov Model," Econometrics, MDPI, vol. 3(2), pages 1-12, March.
    4. 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.
    5. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    6. 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.
    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. Lee, Ji Hyung & Sasaki, Yuya & Toda, Alexis Akira & Wang, Yulong, 2024. "Tuning parameter-free nonparametric density estimation from tabulated summary data," Journal of Econometrics, Elsevier, vol. 238(1).
    9. 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.
    10. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    11. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    12. 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.
    13. 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.
    14. Fabrice Tourre, 2017. "A Macro-Finance Approach to Sovereign Debt Spreads and Returns," 2017 Meeting Papers 13, Society for Economic Dynamics.
    15. 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.
    16. Van Tran, Quang & Kukal, Jaromir, 2024. "Renyi entropy based design of heavy tailed distribution for return of financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    17. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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 qt7g23r5kh, Department of Economics, UC San Diego.
    2. Zhou, Jie, 2009. "The asset location puzzle: Taxes matter," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 955-969, April.
    3. Mankart, Jochen & Rodano, Giacomo, 2015. "Personal bankruptcy law, debt portfolios, and entrepreneurship," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 157-172.
    4. Takefumi Yamazaki, 2018. "Accuracy and speed of the solution methods for sovereign default models: The stable performance of the Tauchen method and cubic spline interpolation," Public Policy Review, Policy Research Institute, Ministry of Finance Japan, vol. 14(4), pages 641-662, July.
    5. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    6. Lapatinas, Athanasios, 2009. "Labour adjustment costs: Estimation of a dynamic discrete choice model using panel data for Greek manufacturing firms," Labour Economics, Elsevier, vol. 16(5), pages 521-533, October.
    7. Christian Bayer & Falko Juessen, 2012. "On the Dynamics of Interstate Migration: Migration Costs and Self-Selection," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 377-401, July.
    8. 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.
    9. Gabriel Ulyssea, 2018. "Firms, Informality, and Development: Theory and Evidence from Brazil," American Economic Review, American Economic Association, vol. 108(8), pages 2015-2047, August.
    10. Christian Bayer, 2009. "A Comment on the Economics of Labor Adjustment: Mind the Gap: Evidence from a Monte Carlo Experiment," American Economic Review, American Economic Association, vol. 99(5), pages 2258-2266, December.
    11. Schündeln, Matthias, 2005. "Modeling Firm Dynamics to Identify the Cost of Financing Constraints in Ghanaian Manufacturing," Proceedings of the German Development Economics Conference, Kiel 2005 29, Verein für Socialpolitik, Research Committee Development Economics.
    12. Kai Du & Steven Huddart, 2020. "Economic persistence, earnings informativeness, and stock return regularities," Review of Accounting Studies, Springer, vol. 25(4), pages 1263-1300, December.
    13. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
    14. Makoto Nakajima, 2009. "Equilibrium Default and Temptation," 2009 Meeting Papers 863, Society for Economic Dynamics.
    15. Moody Chu & Chun-Hung Kuo & Matthew Lin, 2013. "Tensor Spline Approximation in Economic Dynamics with Uncertainties," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 175-198, August.
    16. Makoto Nakajima & José-Víctor Ríos-Rull, 2014. "Credit, Bankruptcy, and Aggregate Fluctuations," NBER Working Papers 20617, National Bureau of Economic Research, Inc.
    17. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    18. Christopher A. Hennessy & Ilya A. Strebulaev, 2020. "Beyond Random Assignment: Credible Inference and Extrapolation in Dynamic Economies," Journal of Finance, American Finance Association, vol. 75(2), pages 825-866, April.
    19. Giulio Fella & Giovanni Gallipoli & Jutong Pan, 2019. "Markov-Chain Approximations for Life-Cycle Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 34, pages 183-201, October.
    20. 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.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:118:y:2013:i:3:p:445-450. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.