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(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle

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  • Klein, Ingo

Abstract

Jaynes (1957a,b) formulates the maximum entropy (ME) principle as the search for a distribution maximizing a given entropy under some given constraints. Kapur (1984) and Kesavan & Kapur (1989) introduce the generalized maximum entropy principle as the derivation of an entropy for which a given distribution has the maximum entropy property under some given constraints. Both principles will be considered for cumulative entropies. Such entropies depend either on the distribution (direct) or on the survival function (residual) or on both (paired). Maximizing this entropy without any constraint gives a extremely U-shaped (= bipolar) distribution. Under the constraint of fixed mean and variance. maximizing the cumulative entropy tries to transform a distribution in the direction of a bipolar distribution as far as it is allowed by the constraints. A bipolar distribution represents so-called contradictory information in contrast to minimum or no information. Only a few maximum entropy distributions for cumulative entropies have already been derived in the literature. We extend the results to well-known flexible distributions (like the generalized logistic distribution) and derive some special distributions (like the skewed logistic, the skewed Tukey λ and the extended Burr XII distribution). The generalized maximum entropy principle will be applied to the generalized Tukey λ distribution and the Fechner family of skewed distributions. At last, cumulative entropies will be estimated such that the data was drawn from a ME distribution. This estimator will be applied to the daily S&P500 returns and the time duration between mine explosions.

Suggested Citation

  • Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    • Handle: RePEc:zbw:iwqwdp:252017
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    References listed on IDEAS

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    1. Park, Sung Y. & Bera, Anil K., 2009. "Maximum entropy autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 150(2), pages 219-230, June.
    2. Georgios Psarrakos & Jorge Navarro, 2013. "Generalized cumulative residual entropy and record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 623-640, July.
    3. Yogesh Mani Tripathi & Amulya Kumar Mahto & Sanku Dey, 2017. "Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution," Annals of Data Science, Springer, vol. 4(1), pages 63-81, March.
    4. Jorge Navarro & Georgios Psarrakos, 2017. "Characterizations based on generalized cumulative residual entropy functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1247-1260, February.
    5. Su, Steve, 2007. "Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i09).
    6. Vikas Kumar, 2017. "Characterization results based on dynamic Tsallis cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8343-8354, September.
    7. P. G. Sankaran & S. M. Sunoj, 2017. "Quantile-based cumulative entropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 805-814, January.
    8. Ilhan Usta, 2013. "Different estimation methods for the parameters of the extended Burr XII distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 397-414, February.
    9. Shao, Quanxi, 2004. "Notes on maximum likelihood estimation for the three-parameter Burr XII distribution," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 675-687, April.
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