Luna Moon <lunamoonmoon@[EMAIL PROTECTED]
> writes:
> Hi all,
>
> How do I introduce correlation to two otherwise standard Poisson
> processes?
Here's one way. Note that the sum of two independent Poisson processes is
a
Poisson process.
If X(t), Y(t) and Z(t) are independent Poisson processes with rates
lambda_x, lambda_y and lambda_z respectively, then X(t) + Y(t) and
X(t) + Z(t) are Poisson processes with rates lambda_x + lambda_y and
lambda_x + lambda_z, and
Cov(X(t)+Y(t), X(t)+Z(t)) = Var(X(t)) = lambda_x
so the correlation coefficient of X(t)+Y(t) and X(t)+Z(t) is
lambda_x/sqrt((lambda_x+lambda_y)(lambda_x+lambda_z)).
--
Robert Israel israel@[EMAIL PROTECTED]
of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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