Numerical integration

Hi:

You could write the function this way:

f <- function(x, xstar, k) dnorm(x) * k * x * (x >= xstar)

where the term in parentheses is a logical. For any x < xstar, f will
be zero by definition. Substitute your density in for dnorm().

To integrate over a grid of (xstar, k) values, you could try this:

# generate a grid of (xstar, k) pairs
pars <- expand.grid(xstar = seq(0, 2, by = 0.2), k = seq(0.5, 2, by = 0.5))

# We modify the function to do the integration and return its value.
# Note that since f = 0 for all x <= xstar, integrating from -Inf to Inf
# yields the same answer as integrating from xstar to Inf.
fun <- function(xstar, k) {
    f <- function(x, xstar, k) dnorm(x) * k * x * (x >= xstar)
    integrate(f, -Inf, Inf, xstar = xstar, k = k)$value
   }

# Method 1: (outputs a data frame)
library(plyr)
out <- mdply(pars, fun)

# Method 2a: (outputs a matrix)
out <- cbind(pars, mapply(fun, xstar = pars[['xstar']], k = pars[['k']]))

# Method 2b: (outputs a data frame)
out <- data.frame(pars, value = mapply(fun, xstar = pars[['xstar']], k
= pars[['k']]))

HTH,
Dennis

Hello!

I know that probably my question is rather simple ?but I' m a very beginner
R-user.

I have to numerically integrate ?the product of two function A(x) and B(x).
The integretion limits are [X*; +inf]

Function A(x) is a pdf function while B(x)=e*x is a linear function whose
value is equal to 0 when the ?x < X*

Moreover I have to iterate this process for different value of X* and for
different pdf of the same type.

I know the comand INTEGRATE but ?I can' t make it work.

Which is the best function to do this and how does it work?

Thank you very much in advanced!!

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thank you very much for your suggestion! 

I tried to do that with the psf I need to use: the 3 parameters Lognormal. I
did that with a single xstar and a single triplet of parameters  to check it
works.[I put some numbers to make it woks , but actually they comes from
statistical analysis]

/# these are the 3 parameters
a<- 414.566
b<- 345.5445
g<- -0.9695679
xstar<- 1397.923
#I create a vector
pars <-expand.grid(xstar = xstar, a= a, b= b , g= g) 
fun <- function(xstar, a,b,g,k) { 
    f <- function(x, xstar, a, b,g,k) f.lognorm(x) * k * x * (x >= xstar) 
    integrate(f, -Inf, Inf, xstar = xstar, a = a, b =b, g=g, k=k)$value 
   } 
# Method 1: (outputs a data frame) 
library(plyr) 
out <- mdply(pars, fun)/ 

at this stage a warning message comes out: *Errore in k > -1e-07 : 'k' is
missing*

Any ideas of why this error come out ? I really don' know.....
Moreover , can I use the algorithm suggested  iteratively by using  a grid
of xstar values and different triplets of parameters ( instead of different
value of k) ?

Thank you so much for any help!! 


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