TY - JOUR
T1 - Recent developments on the construction of bivariate distributions with fixed marginals
AU - Lin, Gwo Dong
AU - Dou, Xiaoling
AU - Kuriki, Satoshi
AU - Huang, Jin Sheng
N1 - Funding Information:
The authors would like to thank the editors and referees for valuable comments and suggestions. The paper was presented at the first conference on Statistical Distributions and Applications (ICOSDA 2013) held from 10th to 12th October 2013 by Central Michigan University, USA. GD Lin would like to thank the Chairs of Organizing Committee, Professor Felix Famoye and Professor Carl Lee, for their kind invitation, and the National Science Council of Taiwan (ROC) for financial support under Grants NSC 99-2118-M-001-003-MY3 and NSC 102-2118-M-001-008-MY2.
Publisher Copyright:
© 2014, Lin et al.; licensee Springer.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee’s distributions, Baker’s distributions and Bayramoglu’s distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2008, SORT) and (ii) the monograph by Balakrishnan and Lai (2009, Springer). Some new results are provided. Mathematics Subject Classification (2000): 62H20; 62H86; 62G30; 60E05; 62E10.
AB - Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee’s distributions, Baker’s distributions and Bayramoglu’s distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2008, SORT) and (ii) the monograph by Balakrishnan and Lai (2009, Springer). Some new results are provided. Mathematics Subject Classification (2000): 62H20; 62H86; 62G30; 60E05; 62E10.
KW - Baker’s distribution
KW - Bayramoglu’s distribution
KW - Bivariate order statistics
KW - Chebyshev’s inequality for integrals
KW - Euler–Maclaurin summation formula
KW - FGM distribution
KW - Fréchet–Hoeffding bounds
KW - Hoeffding’s identity for covariance
KW - Kendall’s tau
KW - Pearson’s correlation
KW - Sarmanov and Lee’s distribution
KW - Spearman’s rho
KW - Weak convergence
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U2 - 10.1186/2195-5832-1-14
DO - 10.1186/2195-5832-1-14
M3 - Review article
AN - SCOPUS:85034067208
SN - 2195-5832
VL - 1
JO - Journal of Statistical Distributions and Applications
JF - Journal of Statistical Distributions and Applications
IS - 1
M1 - 14
ER -