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The Bivariate Burr Distribution

  • Frederick C. Durling
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)

Summary

The bivariate Burr distribution,
$${\text{F(x,y)}}\,{\text{ = }}\,{\text{1}}\, - \,{(1 + {{\text{x}}^{^{_{{{^{\text{b}}}_1}}}}})^{ - {\text{p}}}}\, - \,{(1 + {{\text{y}}^{^{_{^{\text{b}}2}}}})^{ - {\text{p}}}}\, + \,{(1 + {{\text{x}}^{^{_{{{^{\text{b}}}_1}}}}} + {{\text{y}}^{^{_{^{\text{b}}2}}}} + {\text{r}}{{\text{x}}^{^{_{{{^{\text{b}}}_1}}}}}{{\text{y}}^{^{_{^{\text{b}}2}}}})^{ - {\text{p}}}};\,{\text{x,}}\,{\text{y}}\,\underline \geqslant \,0,\,0\,\underline \leqslant \,{\text{r}}\,\underline \leqslant \,{\text{p}}\, + \,1;\,{\text{F(x,y)}}\,{\text{ = }}\,{\text{0}}\,{\text{elsewhere}}$$
is developed and investigated. Two special cases of the distribution occur when the parameter r = 0 and 1 respectively. For the limiting case r = 0, F(x,y) reduces to the bivariate case of the multivariate Burr distribution developed by Takahasi (1965). When r = 1, F(x,y) = F(x)·F(y), the independent case. The relationship of the bivariate Burr distribution and its marginals to the Pearson curves is discussed.

Keywords

Burr distribution general system of distributions Pearson system of frequency curves bivariate Burr distribution 

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Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • Frederick C. Durling
    • 1
  1. 1.University of WaikatoHamiltonNew Zealand

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