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
Integration of mixed normal distribution
3 messages · Johannes Radinger, Rui Barradas, David Winsemius
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,
Rui Barradas
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
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
On Jan 30, 2013, at 4:19 AM, Johannes Radinger wrote:
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)
I think if you check any calculus text you will find a theorem stating that integral( a*f(x) + b*g(x) ) = a*integral(f(x)) + b*integral(g(x))
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?
The application to this problem seems straightforward. The fact that you are using the range of -Inf to x should make the calculations easier.
David Winsemius, MD Alameda, CA, USA