R help - Jun 2007 - Normal and Poisson tail area expectations in R

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.
                                                    Thank you very much.

  
 
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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