R help - Sep 2010 - solve integrate(,..) varying limits of integration

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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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
> ___________________________________________________________
> Neu: WEB.DE De-Mail - Einfach wie E-Mail, sicher wie ein Brief!
> Jetzt De-Mail-Adresse reservieren: https://produkte.web.de/go/demail02
>
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>
-- 
Dimitris Rizopoulos
Assistant Professor
Department of Biostatistics
Erasmus University Medical Center

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