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

Charles C. Berry cberry at tajo.ucsd.edu
Wed Jun 13 23:29:21 CEST 2007

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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