Recent developments on the construction of bivariate distributions with fixed marginals

Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki, Jin Sheng Huang

Research output: Contribution to journalReview article

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number14
JournalJournal of Statistical Distributions and Applications
Volume1
Issue number1
DOIs
Publication statusPublished - 2014 Dec 1

Keywords

  • Baker’s distribution
  • Bayramoglu’s distribution
  • Bivariate order statistics
  • Chebyshev’s inequality for integrals
  • Euler–Maclaurin summation formula
  • FGM distribution
  • Fréchet–Hoeffding bounds
  • Hoeffding’s identity for covariance
  • Kendall’s tau
  • Pearson’s correlation
  • Sarmanov and Lee’s distribution
  • Spearman’s rho
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computer Science Applications

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