# [R] Integration of mixed normal distribution

Wed Jan 30 13:34:25 CET 2013

```Hello,

You could do something like the following.

fun <- function(x, mean, sd1, sd2, p)
dnorm(x, mean, sd1)*p + dnorm(x, mean, sd2)*(1 - p)

fun2 <- function(x1, x2, mean, sd1, sd2, p){
p1 <- pnorm(x2, mean, sd1) - pnorm(x1, mean, sd1)
p2 <- pnorm(x2, mean, sd2) - pnorm(x1, mean, sd2)
p1*p + p2*(1 - p)
}

integrate(fun, 0, 1, mean = 0, sd1 = 1, sd2 = 2, p = 0.5)
fun2(0, 1, mean = 0, sd1 = 1, sd2 = 2, p = 0.5)

Hope this helps,

Em 30-01-2013 09:19, Johannes Radinger escreveu:
> Hi,
>
> I already found a conversation on the integration of a normal
> distribution and two
> suggested solutions
> (https://stat.ethz.ch/pipermail/r-help/2007-January/124008.html):
>
> 1) integrate(dnorm, 0,1, mean = 0, sd = 1.2)
>
> and
>
> 2) pnorm(1, mean = 0, sd = 1.2) - pnorm(0, mean = 0, sd = 1.2)
>
> where the pnorm-approach is supposed to be faster and with higher precision.
>
> I want to integrate a mixed normal distribution like:
> normaldistr_1 * p + normaldistr_2 * (1-p)
>
> where p is between 0 and 1 and the means for both distributions are 0
> but the standard deviations differ.
>
> In addition, I want to get the integrals from x to infinity or from -
> infinity to x for
> the mixed distribution.
>
> Can that be done with high precision in R and if yes how?
>
> best regards,
>
> Johannes
>
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