IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-021-00274-z.html
   My bibliography  Save this article

Classical and Bayesian Estimation of Entropy for Pareto Distribution in Presence of Outliers with Application

Author

Listed:
  • Amal S. Hassan

    (Faculty of Graduate Studies for Statistical Research)

  • E. A. Elsherpieny

    (Faculty of Graduate Studies for Statistical Research)

  • Rokaya E. Mohamed

    (Faculty of Graduate Studies for Statistical Research)

Abstract

The measure of entropy has a pivotal role in the information theory area. In this paper, estimation of differential entropy for Pareto distribution in presence of r outliers is considered. In this regard, the classical and Bayesian estimation techniques of differential entropy are employed. In classical setup, we obtain the maximum likelihood estimators of the differential entropy as well as assessing their performance via a simulation study. The entropy Bayesian estimator is derived using squared error, linear exponential, weighted squared error and K loss functions. The Metropolis-Hastings algorithm is used to generate posterior random variables. Monte Carlo simulations are designed to implement the precision of estimates for different sample sizes and number of outliers. Furthermore, performance of estimates is planned by experiments with real data. Generally, we conclude that the entropy Bayesian estimates of simulated data tend to the true value as the number of outliers increases. Further, the entropy Bayesian estimate under weighted squared error loss function is preferable to the other estimates in majority of situations.

Suggested Citation

  • Amal S. Hassan & E. A. Elsherpieny & Rokaya E. Mohamed, 2023. "Classical and Bayesian Estimation of Entropy for Pareto Distribution in Presence of Outliers with Application," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 707-740, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00274-z
    DOI: 10.1007/s13171-021-00274-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-021-00274-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-021-00274-z?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. Mehdi Jabbari Nooghabi, 2016. "Estimation of the Lomax Distribution in the Presence of Outliers," Annals of Data Science, Springer, vol. 3(4), pages 385-399, December.
    2. M. Jabbari Nooghabi & E. Khaleghpanah Nooghabi, 2016. "On entropy of a Pareto distribution in the presence of outliers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5234-5250, September.
    3. H. Malik, 1970. "Estimation of the parameters of the Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 15(1), pages 126-132, December.
    4. Zeinab Amin, 2008. "Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1203-1217.
    5. Varian, Hal R, 1975. "A Third Remark on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 43(5-6), pages 985-986, Sept.-Nov.
    6. Ulhas Dixit, 1994. "Bayesian approach to prediction in the presence of outliers for Weibull distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 127-136, December.
    7. S. Baratpour & J. Ahmadi & N. Arghami, 2007. "Entropy properties of record statistics," Statistical Papers, Springer, vol. 48(2), pages 197-213, 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. Mehdi Jabbari Nooghabi, 2016. "Estimation of the Lomax Distribution in the Presence of Outliers," Annals of Data Science, Springer, vol. 3(4), pages 385-399, December.
    2. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    3. Elfessi, Abdulaziz & Chun Jin, 1996. "On robust estimation of the common scale parameter of several Pareto distributions," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 345-352, September.
    4. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    5. Mehdi Jabbari Nooghabi, 2021. "Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    6. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    7. Covarrubias, Enrique, 2013. "Global invertibility of excess demand functions," MPRA Paper 47300, University Library of Munich, Germany.
    8. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2023. "On the three-component mixture of exponential distributions: A Bayesian framework to model data with multiple lower and upper outliers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 480-500.
    9. Jorge Iván González, 2016. "Sentimientos y racionalidad en economía," Books, Universidad Externado de Colombia, Facultad de Economía, edition 1, number 75.
    10. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    11. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    12. Sangun Park & Johan Lim, 2015. "On censored cumulative residual Kullback–Leibler information and goodness-of-fit test with type II censored data," Statistical Papers, Springer, vol. 56(1), pages 247-256, February.
    13. Kumar, Vikas, 2016. "Some results on Tsallis entropy measure and k-record values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 667-673.
    14. Christensen, Finn & Cornwell, Christopher R., 2018. "A strong correspondence principle for smooth, monotone environments," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 15-24.
    15. Fu, Jiayu & Xu, Ancha & Tang, Yincai, 2012. "Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1829-1836.
    16. M. El-Din & A. Shafay, 2013. "One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data," Statistical Papers, Springer, vol. 54(2), pages 287-307, May.
    17. Kaizoji, Taisei, 2010. "Multiple equilibria and chaos in a discrete tâtonnement process," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 597-599, December.
    18. Ayush Tripathi & Umesh Singh & Sanjay Kumar Singh, 2021. "Inferences for the DUS-Exponential Distribution Based on Upper Record Values," Annals of Data Science, Springer, vol. 8(2), pages 387-403, June.
    19. Saverio M. Fratini, 2008. "Economic Generality Versus Mathematical Genericity: Activity‐Level Indeterminacy And The Index Theorem In Constant Returns Production Economies," Metroeconomica, Wiley Blackwell, vol. 59(2), pages 266-275, May.
    20. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).

    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:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00274-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.