IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i2d10.1007_s11749-021-00789-5.html
   My bibliography  Save this article

Stochastic monotonicity of dependent variables given their sum

Author

Listed:
  • Franco Pellerey

    (Politecnico di Torino)

  • Jorge Navarro

    (Universidad de Murcia)

Abstract

Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.

Suggested Citation

  • Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:2:d:10.1007_s11749-021-00789-5
    DOI: 10.1007/s11749-021-00789-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00789-5
    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/s11749-021-00789-5?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. Hu, Taizhong & Hu, Jinjin, 1999. "Sufficient conditions for negative association of random variables," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 167-173, November.
    2. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    3. J. George Shanthikumar & David D. Yao, 1987. "Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks," Operations Research, INFORMS, vol. 35(4), pages 583-588, August.
    4. Hwang, Gene T. & Stefanski, Leonard A., 1994. "Monotonicity of regression functions in structural measurement error models," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 113-116, May.
    5. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    6. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    7. Jorge Navarro & Julio Mulero, 2020. "Comparisons of coherent systems under the time-transformed exponential model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 255-281, March.
    8. Yasushi Masuda, 1995. "Exploiting Partial Information in Queueing Systems," Operations Research, INFORMS, vol. 43(3), pages 530-536, June.
    9. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    10. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
    11. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    12. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    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. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of independent discrete losses in large pools," LIDAM Discussion Papers ISBA 2023010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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. Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    2. Jamison Dean T. & Jamison Julian, 2011. "Characterizing the Amount and Speed of Discounting Procedures," Journal of Benefit-Cost Analysis, De Gruyter, vol. 2(2), pages 1-56, April.
    3. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    4. Dean T. Jamison & Julian Jamison, 2010. "Characterizing the amount and speed of discounting procedures," Working Papers 10-14, Federal Reserve Bank of Boston.
    5. Juan Pablo Atal & José Ignacio Cuesta & Felipe González & Cristóbal Otero, 2024. "The Economics of the Public Option: Evidence from Local Pharmaceutical Markets," American Economic Review, American Economic Association, vol. 114(3), pages 615-644, March.
    6. Péter Eso & Balázs Szentes, 2004. "The Price of Advice," Discussion Papers 1416, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    8. Bagdonavicius, Vilijandas & Nikulin, Mikhail, 2000. "On goodness-of-fit for the linear transformation and frailty models," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 177-188, April.
    9. Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    10. Alexandre de Corniere, 2013. "Search Advertising," Economics Series Working Papers 649, University of Oxford, Department of Economics.
    11. Andrew Rhodes & Jidong Zhou, 2019. "Consumer Search and Retail Market Structure," Management Science, INFORMS, vol. 67(6), pages 2607-2623, June.
    12. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    13. Chakravarty, Surajeet & Kaplan, Todd R. & Myles, Gareth, 2018. "When costly voting is beneficial," Journal of Public Economics, Elsevier, vol. 167(C), pages 33-42.
    14. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    15. K. Motarjem & M. Mohammadzadeh & A. Abyar, 2020. "Geostatistical survival model with Gaussian random effect," Statistical Papers, Springer, vol. 61(1), pages 85-107, February.
    16. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    17. Péter Eső & Balázs Szentes, 2007. "The price of advice," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 863-880, December.
    18. Rhodes, Andrew, 2011. "Multiproduct pricing and the Diamond Paradox," MPRA Paper 32511, University Library of Munich, Germany.
    19. Nocke, Volker & Peitz, Martin & Rosar, Frank, 2011. "Advance-purchase discounts as a price discrimination device," Journal of Economic Theory, Elsevier, vol. 146(1), pages 141-162, January.
    20. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.

    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:testjl:v:31:y:2022:i:2:d:10.1007_s11749-021-00789-5. 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.