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

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Wed, 13 Jun 2007 18:58:15 -0400

More interesting is the Poisson convolution. I don't know if there is an analytic solution to this. I looked at Jolley's "Summation of Series" and Abramowitz and Stegun, but no help there. It seems that discrete FFT technique should work. Does anyone know the answer?

Ravi.



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  



-----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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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.

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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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