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

From: Charles C. Berry <cberry_at_tajo.ucsd.edu>
Date: Thu, 14 Jun 2007 10:35:36 -0700

Ravi,

This looks simple to me.

km_G <- function(lambda,k)

 	lambda*ppois(k-1,lambda,lower=FALSE) -
 		k*ppois(k,lambda,lower=FALSE)

Am I confused here?

Chuck

On Wed, 13 Jun 2007, Ravi Varadhan wrote:

>
> 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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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. Received on Thu 14 Jun 2007 - 17:47:40 GMT

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