The Bivariate Burr Distribution

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