IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v143y2016icp194-207.html
   My bibliography  Save this article

Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal

Author

Listed:
  • Balakrishnan, Narayanaswamy
  • Ristić, Miroslav M.

Abstract

In this paper, we introduce two new families of multivariate distributions with finite or infinite support above or below the diagonal generated by McKay’s bivariate gamma distribution and show that their conditional distributions are univariate gamma- and beta-generated distributions. We derive the Shannon entropies of the introduced families of bivariate distributions. We then focus on the special cases of bivariate gamma-exponentiated exponential distributions, and discuss their properties. Finally, we illustrate the usefulness of the proposed bivariate gamma-exponentiated exponential distributions with a real dataset.

Suggested Citation

  • Balakrishnan, Narayanaswamy & Ristić, Miroslav M., 2016. "Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 194-207.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:194-207
    DOI: 10.1016/j.jmva.2015.09.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15002262
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.09.012?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. Balakrishna, N. & Shiji, K., 2014. "On a class of bivariate exponential distributions," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 153-160.
    2. Manuel Franco & José Ruiz, 2001. "Characterizations of discrete distributions based on conditional expectations of record values," Statistical Papers, Springer, vol. 42(1), pages 101-110, January.
    3. M. C. Jones & P. V. Larsen, 2004. "Multivariate distributions with support above the diagonal," Biometrika, Biometrika Trust, vol. 91(4), pages 975-986, December.
    4. Josep L. Carrasco & Lluís Jover, 2003. "Estimating the Generalized Concordance Correlation Coefficient through Variance Components," Biometrics, The International Biometric Society, vol. 59(4), pages 849-858, December.
    5. Furman, Edward, 2008. "On a multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2353-2360, October.
    6. A. Mathal & P. Moschopoulos, 1992. "A form of multivariate gamma distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 97-106, March.
    7. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    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. Vadim Semenikhine & Edward Furman & Jianxi Su, 2018. "On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance," Risks, MDPI, vol. 6(3), pages 1-20, August.
    2. Shyamal Ghosh & Prajamitra Bhuyan & Maxim Finkelstein, 2022. "On a bivariate copula for modeling negative dependence: application to New York air quality data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1329-1353, December.
    3. M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    4. Sulewski Piotr & Szymkowiak Magdalena, 2022. "The Weibull lifetime model with randomised failure-free time," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 59-76, December.

    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. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    2. Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
    3. Zhou, Ming & Dhaene, Jan & Yao, Jing, 2018. "An approximation method for risk aggregations and capital allocation rules based on additive risk factor models," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 92-100.
    4. Christian Caamaño-Carrillo & Javier E. Contreras-Reyes, 2022. "A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    5. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    6. Arjun Gupta & Jacek Wesolowski, 1997. "Uniform Mixtures Via Posterior Means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 171-180, March.
    7. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.
    8. Chatenet, Q. & Remy, E. & Gagnon, M. & Fouladirad, M. & Tahan, A.S., 2021. "Modeling cavitation erosion using non-homogeneous gamma process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    9. Helenowski Irene B & Vonesh Edward F & Demirtas Hakan & Rademaker Alfred W & Ananthanarayanan Vijayalakshmi & Gann Peter H & Jovanovic Borko D, 2011. "Defining Reproducibility Statistics as a Function of the Spatial Covariance Structures in Biomarker Studies," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-21, January.
    10. Axel Bücher & Ivan Kojadinovic, 2019. "A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1145-1165, September.
    11. Lee, Sangyeol & Oh, Haejune, 2015. "Entropy test and residual empirical process for autoregressive conditional duration models," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 1-12.
    12. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    13. Furman, Edward, 2008. "On a multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2353-2360, October.
    14. C. Paddy Farrington & Mounia N. Hocine, 2010. "Within‐individual dependence in self‐controlled case series models for recurrent events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 457-475, May.
    15. Zacharias Psaradakis & Marián Vávra, 2017. "Normality Tests for Dependent Data: Large-Sample and Bootstrap Approaches," Birkbeck Working Papers in Economics and Finance 1706, Birkbeck, Department of Economics, Mathematics & Statistics.
    16. Derek S. Young & Xi Chen & Dilrukshi C. Hewage & Ricardo Nilo-Poyanco, 2019. "Finite mixture-of-gamma distributions: estimation, inference, and model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1053-1082, December.
    17. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    18. Székely, Gábor J. & Rizzo, Maria L., 2004. "Mean distance test of Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 241-247, April.
    19. Graciela Boente & Daniela Rodriguez & Wenceslao González Manteiga, 2014. "Goodness-of-fit Test for Directional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 259-275, March.
    20. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.

    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:eee:jmvana:v:143:y:2016:i:c:p:194-207. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.