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A versatile bivariate distribution on a bounded domain: Another look at the product moment correlation

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  • Samuel Kotz
  • J. Renevan Dorp

Abstract

The Farlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGMs with continuous marginals on a bounded support discussed in the literature are only those with uniform or power marginals. In this paper we study the bivariate FGM family with marginals given by the recently proposed two-sided power (TSP) distribution. Since this family of bounded continuous distributions is very flexible, the properties of the FGM family with TSP marginals could serve as an indication of the structure of the FGM distribution with arbitrary marginals defined on a compact set. A remarkable stability of the correlation between the marginals has been observed.

Suggested Citation

  • Samuel Kotz & J. Renevan Dorp, 2002. "A versatile bivariate distribution on a bounded domain: Another look at the product moment correlation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1165-1179.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:8:p:1165-1179
    DOI: 10.1080/0266476022000011247
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    References listed on IDEAS

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    1. V. Barnett, 1985. "The Bivariate Exponential Distribution; A Review And Some New Results," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 343-356, December.
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    Cited by:

    1. Hernández-Bastida, A. & Fernández-Sánchez, M.P. & Gómez-Déniz, E., 2009. "The net Bayes premium with dependence between the risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 247-254, October.
    2. Agustín Hernández-Bastida & M. Fernández-Sánchez, 2012. "A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 391-409, November.
    3. Fernández Mariela & Kolev Nikolai, 2007. "Bivariate Density Classification by the Geometry of the Marginals," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 3-18, January.

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