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I'm having trouble to compute and then plot multiple integral. It would be great if you could help me.

So I have this function 

> f = function(x, mu = 30, s = 12){dnorm(x, mu, s)}

which i want to integrate multiple time between z(1:100) to +Inf to plot that with x=z and y = auc :

> auc = Integrate(f, z, Inf)

R return : 

Warning message:
In if (is.finite(lower)) { :
  the condition has length > 1 and only the first element will be used

I have tested to do a loop : 

while(z < 100){
z = 1
auc = integrate(f,z,Inf)
z = z+1}

Doesn't work either ... don't know what to do

(I'm new to R , so I'm already sorry if it is really easy .. )

Thanks for your help :) !

Dason
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Boo
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2 Answers2

4

There is no need to do the integrating by hand. pnorm gives the integral from negative infinity to the input for the normal density. You can get the upper tail instead by modifying the lower.tail parameter

z <- 1:100
y <- pnorm(z, mean = 30, sd = 12, lower.tail = FALSE)
plot(z, y)

If you're looking to integrate more complex functions then using integrate will be necessary - but if you're just looking to find probabilities for distributions then there will most likely be a function built in that does the integration for you directly.

Dason
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  • Oh , ok, I understand more the first one, but yours seems more elegant ... Thanks a lot :) – Boo Mar 08 '14 at 20:25
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Your problem is actually somewhat subtle, and in a certain sense gets to the core of how R works, so here is a slightly longer explanation.

R is a "vectorized" language, which means that just about everything works on vectors. If I have 2 vectors A and B, then A+B is the element-by-element sum of A and B. Nearly all R functions work this way also. If X is a vector, then Y <- exp(X) is also a vector, where each element of Y is the exponential of the corresponding element of X.

The function integrate(...) is one of the few functions in R that is not vectorized. So when you write:

f   <- function(x, mu = 30, s = 12){dnorm(x, mu, s)}
auc <- integrate(f, z, Inf)

the integrate(...) function does not know what to do with z when it is a vector. So it takes the first element and complains. Hence the warning message.

There is a special function in R, Vectorize(...) that turns scalar functions into vectorized functions. You would use it this way:

f   <- function(x, mu = 30, s = 12){dnorm(x, mu, s)}
auc <- Vectorize(function(z) integrate(f,z,Inf)$value)
z   <- 1:100
plot(z,auc(z), type="l")   # plot lines

jlhoward
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