have a look at uniroot(), e.g.,
ff <- function (low, r, s) {
f <- function (t, r, s) {
exp(-(s^2 - 2*r*s*t + t^2) / (2*(1-r^2))) / (2*pi*sqrt(1-r^2))
}
integrate(f, low, Inf, r = r, s = s)$value - 0.05
}
uniroot(ff, c(-3, -2), r = 0.730163, s = -2)$root
I hope it helps.
Best,
Dimitris
On 9/14/2010 9:15 AM, Tonja Krueger wrote:
Dear List,
Is there a way to solve
integrate(func.1,x, Inf) $value =0.05
by varying the lower limit of integration (x in the example above)?
So far I got:
r<- 0.730163
s<--2
func.1<- function(t)
{1/(2*pi*sqrt(1-r^2))*exp(-1/(2*(1-r^2))*(s^2-2*r*s*t+t^2))}
I can change the lower limit manually, like:
integrate(func.1, -2.5, Inf) $value
[1] 0.05053265
integrate(func.1, -2.4, Inf) $value
[1] 0.04942731
integrate(func.1, -2.45, Inf) $value
[1] 0.05000923
but this is very time-consuming. So I was wondering if there is a better,
preferably an automated way to solve the equation?
Thanks,
Tonja
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--
Dimitris Rizopoulos
Assistant Professor
Department of Biostatistics
Erasmus University Medical Center
Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
Tel: +31/(0)10/7043478
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