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Discrete approximations of continuous probability distributions obtained by minimizing Cramér-von Mises-type distances

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  • Alessandro Barbiero

    (Università degli Studi di Milano)

  • Asmerilda Hitaj

    (Università degli Studi dell’Insubria)

Abstract

We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F(x), by means of k points, $$x_1

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01356-2
    DOI: 10.1007/s00362-022-01356-2
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    References listed on IDEAS

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    1. L. Baringhaus & N. Henze, 2017. "Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 167-188, April.
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    3. 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.
    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 qt7g23r5kh, Department of Economics, UC San Diego.
    5. Farshid Jamshidian & Yu Zhu, 1996. "Scenario Simulation: Theory and methodology (*)," Finance and Stochastics, Springer, vol. 1(1), pages 43-67.
    6. Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    7. Konstantin Pavlikov & Stan Uryasev, 2018. "CVaR distance between univariate probability distributions and approximation problems," Annals of Operations Research, Springer, vol. 262(1), pages 67-88, March.
    8. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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