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The Bivariate Normal Distribution - gatech.edu
The Bivariate Normal Distribution Most of the following discussion is taken from Wilks, Statistical Methods in the Atmospheric Sci- ences, section First, lets define the Bivariate Normal Distribution for two related, normally distributed variables x N ( x , x2 ), and x N ( y , y2 ). Then, the Bivariate Normal Distribution is defined by the following probability density function: " " ##. x x 2 y y 2 x x x y . 1 1. f (x, y) = exp + 2 . 2(1 2 ). p 2 x y 1 2 x y x y (1). The Bivariate Normal PDF difines a surface in the x y plane (see Figure 1). Like its one dimensional counterpart, the Bivariate Normal Distribution has the following properties: Z Z.
ences, section 4.5. First, lets define the bivariate normal distribution for two related, normally distributed variables x ∼ N(µ x,σ2), and x ∼ N(µy,σ2 y). Then, the bivariate normal distribution is defined by the following probability density function: f(x,y) = 1 2πσxσy p 1 −ρ2 exp " − 1 2(1 −ρ2) " x−µx σx 2 + y −µy ...
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