[R] Integral of function of dnorm

[Moshe Olshansky]

Yes, this can be easily computed analytically (even though my result is a bit different).

--- On Fri, 12/2/10, davidr at rhotrading.com <davidr at rhotrading.com> wrote:

> From: davidr at rhotrading.com <davidr at rhotrading.com>
> Subject: Re: [R] Integral of function of dnorm
> To: "Greg Snow" <Greg.Snow at imail.org>, "Trafim Vanishek" <rdapamoga at gmail.com>, "Peter Dalgaard" <p.dalgaard at biostat.ku.dk>
> Cc: r-help at r-project.org
> Received: Friday, 12 February, 2010, 7:35 AM
> and it can be done analytically: =
> -(1 + log(2 pi)) / 2
> 
> -- David L. Reiner
> 
> -----Original Message-----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org]
> On Behalf Of Greg Snow
> Sent: Thursday, February 11, 2010 11:58 AM
> To: Trafim Vanishek; Peter Dalgaard
> Cc: r-help at r-project.org
> Subject: Re: [R] Integral of function of dnorm
> 
> Try:
> 
> > tmpfun <- function(x)
> dnorm(x,mean=8,sd=1)*log(dnorm(x,mean=8,sd=1))
> > integrate( tmpfun, -Inf, Inf)
> 
> Also you may want to look at the log argument to dnorm
> rather than
> taking the log of the function.
> 
> Hope this helps,
> 
> -- 
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow at imail.org
> 801.408.8111
> 
> 
> > -----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 9:49 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,
> > 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 both
> > > directions. If you meant otherwise, please tell
> us what you meant...
> > >
> > 
> >     [[alternative HTML version
> deleted]]
> > 
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