[R] Normal and Poisson tail area expectations in R

[Ravi Varadhan]

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.
>
>
>
> ---------------------------------
> Sucker-punch spam with award-winning protection.
>
>  [[alternative HTML version deleted]]
>
> ______________________________________________
> 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.
>

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




       
---------------------------------


	[[alternative HTML version deleted]]

______________________________________________
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.