# Re: [R] Normal and Poisson tail area expectations in R

Date: Wed, 13 Jun 2007 18:58:15 -0400

Ravi.

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

-----Original Message-----
From: r-help-bounces_at_stat.math.ethz.ch
[mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of kavindra malik Sent: Wednesday, June 13, 2007 5:45 PM
To: Charles C. Berry
Cc: r-help_at_stat.math.ethz.ch
Subject: Re: [R] Normal and Poisson tail area expectations in R

Thank you very much. This solves the problem I was trying to solve. I am new to R and am learning. A great lesson in the power of R...

"Charles C. Berry" <cberry_at_tajo.ucsd.edu> wrote: On Wed, 13 Jun 2007, kavindra malik wrote:

> I am interested in R functions for the following integrals / sums
(expressed best I can in text) -
>
> Normal: G_u(k) = Integration_{Lower limit=k}^{Upper limit=infinity} [(u
-k) f(u) d(u)], where where u is N(0,1), and f(u) is the density function. >
> Poisson: G(lambda,k) = Sum_{Lower limit=k}^{Upper limit=infinity} [(x-k)
p(x, lambda)] where P(x,lambda) is the Poisson prob function with parameter lambda.

```>
```

> The Normal expression is very commonly used in inventory management to
> determine safety stocks (and its tabular values can be found in some
> texts) - and I am also looking for Poisson and/or Gamma as that'd fit
> the situation better.
>
> I am wondering if there are standard functions in R that might allow me to
get these values, instead of needing to do the numerical integration, etc. myself.

Not that I know of, but it is not difficult to do the integration:

> k <- 1.1 # for example
> integrate(function(x) (x-k)*dnorm(x),lower=k,upper=Inf)
0.06861951 with absolute error < 5.5e-07 >

see

```  ?integrate
?qnorm
?qpois
?qgamma

>                                                    Thank you very much.

>
>
>

> ---------------------------------

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>
```Charles C. Berry                            (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cberry_at_tajo.ucsd.edu             UC San Diego
```
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901

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R-help_at_stat.math.ethz.ch 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.

R-help_at_stat.math.ethz.ch 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. Received on Wed 13 Jun 2007 - 23:05:14 GMT

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