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integrating a bivariate normal
*To*: mathgroup at smc.vnet.net
*Subject*: [mg13704] integrating a bivariate normal
*From*: Dennis Swaney <dennis at shrubbery.com>
*Date*: Wed, 19 Aug 1998 01:38:02 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Dear Mathgroup-
Is it me, or is Mathematica incapable of integrating the bivariate
normal distribution if the variables are correlated?
First, I tried the following (integrating the pdf for uncorrelated
variables):
Integrate[Exp[-1/2*(((x - m1)/s1 )^2 +
((y - m2)/s2)^2)]/(2*Pi*Sqrt[s1^2]* Sqrt[s2^2]),
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}]
and it produced the correct answer (1). Next, I tried integrating the
pdf for nonzero r:
Integrate[Exp[-1/(2(1-r^2))*(((x - m1)/s1 )^2 +
((y - m2)/s2)^2-2 r((x - m1)/s1 ) ((y - m2)/s2 ))]/(
2*Pi*Sqrt[s1^2]* Sqrt[s2^2]*Sqrt[1-r^2]),
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}]
and it produced a long, erroneous result (a function of x, which is a
variable of integration!)
Is it possible that the problem results because Abs(r) should be < 1?
If so, how can I specify this condition?
thanks
-Dennis
Dennis P. Swaney
email: Dennis at shrubbery.com
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