R help - Feb 2007 - returns from dnorm and dmvnorm

Hi All,
Why would calls to dnorm and dmvnorm return values that are above 1? For
example,
> dnorm(0.00003,mean=0, sd=0.1)
[1] 3.989423

This is happening on two different installations of R that I have.

Thank you.

Hailu

	[[alternative HTML version deleted]]

well, nobody said that the density must be smaller than 1, right? :-)

it's just the value of the normal density function at the point you  
asked. you may try doing that by hand and, with the correct math,  
you'll get the same thing.

b

On Feb 26, 2007, at 3:03 PM, A Hailu wrote:
> Hi All,
> Why would calls to dnorm and dmvnorm return values that are above  
> 1? For
> example,
>> dnorm(0.00003,mean=0, sd=0.1)
> [1] 3.989423
>
> This is happening on two different installations of R that I have.
>
> Thank you.
>
> Hailu

I guarantee that it would also happen on all future versions of R.

Why would you expect density to be smaller than 1?  The only constraints on
density are that (a) it is non-negative and (b) it integrates to one. The
smaller the variance, the greater the density is around its center.  Density
can be made to become arbitrarily large by letting the variance gets close
to zero, and in the limit you will obtain Dirac's delta function.  


Ravi. 

----------------------------------------------------------------------------
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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of A Hailu
Sent: Monday, February 26, 2007 3:04 PM
To: r-help at stat.math.ethz.ch
Subject: [R] returns from dnorm and dmvnorm

Hi All,
Why would calls to dnorm and dmvnorm return values that are above 1? For
example,
> dnorm(0.00003,mean=0, sd=0.1)
[1] 3.989423

This is happening on two different installations of R that I have.

Thank you.

Hailu

	[[alternative HTML version deleted]]

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On Feb 26, 2007, at 3:03 PM, A Hailu wrote:
> Hi All,
> Why would calls to dnorm and dmvnorm return values that are above  
> 1? For
> example,
>> dnorm(0.00003,mean=0, sd=0.1)
> [1] 3.989423
Because dnorm gives you the density function, whose integral is the  
distribution function, which is likely what you want. Try:

pnorm(0.00003,mean=0, sd=0.1)
> This is happening on two different installations of R that I have.
>
> Thank you.
>
> Hailu
Haris Skiadas
Department of Mathematics and Computer Science
Hanover College