IDEAS home Printed from https://ideas.repec.org/p/zbw/iwqwdp/252017.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/172461/1/1008785520.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    4. 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).
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Tahmasebi Saeid & Parsa Hojat, 2019. "Notes on Cumulative Entropy as a Risk Measure," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 1-7, June.
    2. Suchandan Kayal, 2018. "On Weighted Generalized Cumulative Residual Entropy of Order n," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 487-503, June.
    3. Antonio Di Crescenzo & Suchandan Kayal & Abdolsaeed Toomaj, 2019. "A past inaccuracy measure based on the reversed relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 607-631, July.
    4. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    5. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    6. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti, 2014. "Optimal strategies for selecting project portfolios using uncertain value estimates," European Journal of Operational Research, Elsevier, vol. 233(3), pages 772-783.
    7. Shahzad Hussain & Sajjad Haider Bhatti & Tanvir Ahmad & Muhammad Ahmed Shehzad, 2021. "Parameter estimation of the Pareto distribution using least squares approaches blended with different rank methods and its applications in modeling natural catastrophes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(2), pages 1693-1708, June.
    8. Carol Alexander & José María Sarabia, 2012. "Quantile Uncertainty and Value‐at‐Risk Model Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1293-1308, August.
    9. Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    10. Tahmasebi, Saeid & Eskandarzadeh, Maryam, 2017. "Generalized cumulative entropy based on kth lower record values," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 164-172.
    11. Kumar, Vikas & Rekha,, 2018. "A quantile approach of Tsallis entropy for order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 916-928.
    12. Domenico Di Gangi & Fabrizio Lillo & Davide Pirino, 2015. "Assessing systemic risk due to fire sales spillover through maximum entropy network reconstruction," Papers 1509.00607, arXiv.org, revised Jul 2018.
    13. Amal S. Hassan & Salwa M. Assar & Kareem A. Ali & Heba F. Nagy, 2021. "Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 171-189, December.
    14. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.
    15. Di Gangi, Domenico & Lillo, Fabrizio & Pirino, Davide, 2018. "Assessing systemic risk due to fire sales spillover through maximum entropy network reconstruction," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 117-141.
    16. Sung Y. Park & Anil K. Bera, 2018. "Information theoretic approaches to income density estimation with an application to the U.S. income data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(4), pages 461-486, December.
    17. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.
    18. Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    19. Gersbach, Hans & Liu, Yulin & Tischhauser, Martin, 2021. "Versatile forward guidance: escaping or switching?," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    20. Salman A Rahman & Sheila K West & Harran Mkocha & Beatriz Munoz & Travis C Porco & Jeremy D Keenan & Thomas M Lietman, 2015. "The Distribution of Ocular Chlamydia Prevalence across Tanzanian Communities Where Trachoma Is Declining," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 9(3), pages 1-8, March.

    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:zbw:iwqwdp:252017. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vierlde.html .

    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.