[R] Integral of function of dnorm

Charles Annis, P.E. charles.annis at statisticalengineering.com
Thu Feb 11 18:24:34 CET 2010

Here's a suggestion:  Plot the function:

x <- seq(3, 13, length=101)
plot(x, y=dnorm(x, mean=8,sd=1)*log(dnorm(x,mean=8,sd=1)))

x <- seq(7.5, 8.5, length=101)
plot(x, y=dnorm(x, mean=8,sd=1)*log(dnorm(x,mean=8,sd=1)))

x <- seq(7.9, 8.1, length=101)
plot(x, y=dnorm(x, mean=8,sd=1)*log(dnorm(x,mean=8,sd=1)))

This suggests to me that you can integrate over restricted domains of x, and
sum the intermediate results.

Charles Annis, P.E.

Charles.Annis at StatisticalEngineering.com

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Trafim Vanishek
Sent: Thursday, February 11, 2010 11:49 AM
To: Peter Dalgaard
Cc: r-help at r-project.org
Subject: Re: [R] Integral of function of dnorm

This is exactly what I mean.

I need to find integrate(dnorm(mean=8,sd=1)*log(dnorm(mean=8,sd=1)), -Inf,

Which doesn't work like that, because it says:
Error in dnorm(mean = 8, sd = 1) : element 1 is empty;
   the part of the args list of '.Internal' being evaluated was:
   (x, mean, sd, log)

So how can I define x?
THanks a lot

>  Dear all,
>> How is it possible in R to calculate the following integral:
>> Integral(-Inf, Inf)[log(dnorm(mean = 3, sd = 1))]
>> how can I define that the density dnorm is taken on (-Inf, Inf)
>> Thanks a lot!
> Er, if you mean integral with respect to the x argument in dnorm, then the
> answer is -Inf because log(dnorm(x,...)) goes quadratically to -Inf in
> directions. If you meant otherwise, please tell us what you meant...

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