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

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  • 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.

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  • 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
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    1. 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.
    2. Balakrishna, N. & Shiji, K., 2014. "On a class of bivariate exponential distributions," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 153-160.
    3. 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.
    4. Furman, Edward, 2008. "On a multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2353-2360, October.
    5. 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.
    6. 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.
    7. M. C. Jones & P. V. Larsen, 2004. "Multivariate distributions with support above the diagonal," Biometrika, Biometrika Trust, vol. 91(4), pages 975-986, December.
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    Cited by:

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    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. Sulewski Piotr & Szymkowiak Magdalena, 2022. "The Weibull lifetime model with randomised failure-free time," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 59-76, December.
    4. 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.

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