Re: How to get the analytical PDF of this expression?
- From: Duncan Muirhead <noone@xxxxxxxxxxxx>
- Date: Thu, 13 Jul 2006 12:57:47 +0100
On Thu, 13 Jul 2006 02:08:33 -0700, glare22 wrote:
Can anyone tell me the pdf of this expression u0+u1*x+u2(x^2-1)?If we assume u2>0 then
where u0,u1,u2 is constant. And x is a random variable satisfing the
normal distribution N(0,1). Thanks a lot.
u0 + u1*x + u2*(x*x-1) = u2*y^2 + u0 - u1*u1/(4*u2) - u2
where y = x-u1/(2*u2) is a N(-u1/(2*u2), 1) variable.
y^2 has a non-central chi-square distribution with 1
degree of freedom, whose distribution function you can
find by searching the web (for non-central chi-square),
and then a linear transformation will get the distribution
of the variable you want.
Duncan
.
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