For loop over a function to get function output in R

Question

I want to compute the integral of a function associated with each value in a vector. Using an example, I precisely describe my aim as follows.

Suppose x and y are independent random variables, and I is an indicator variables such that I=1 if y > 0.25x or zero otherwise. I want to make n draws of y from an exponential distribution, and for each draw I wish to compute the integral of g = xf(x)I over the distribution of x, f(x). I want this distribution to be exponential with parameter value of 1. I tried the following code in r.

f = function(n){
  h = list()
  g = numeric()
  y = rexp(n)
  for(i in 1:n){
    h[i] = function(x){(x * dexp(x) * (y[i] > 0.5*x))}
    g[i] = integrate(h[i], lower=-Inf, upper=Inf)
  }
  return(summary(g))
}

But then when I run f(3) I get an error message "*Error in h[i] = function(x) { : cannot coerce type 'closure' to vector of type 'list'"*. But when I run the following codes

y = rexp(1)
h = function(x){x * dexp(x) * (y > 0.5*x)}
integrate(h, lower=-Inf, upper=Inf)
f(3)

I get results. Does somebody has suggestion on how to improve this code so that h function is evaluated at each values of y with the output being a function, which then will be passed to the g function?

Try using [[ to index your list rather than [, ie h[[i]] — James
– James, Commented Nov 11, 2013 at 11:55

Thilo · Accepted Answer · 2013-11-11 11:57:00Z

1

I would suggest to use sapply instead of the loop:

f = function(n){
  y = rexp(n)
  g = sapply(1:n, function(i) 
                  integrate(function(x) (x * dexp(x) * (y[i] > 0.5*x)), lower=-Inf, upper=Inf))
  return(summary(g))
}

answered Nov 11, 2013 at 11:57

Thilo

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2 Comments

csgillespie Over a year ago

Why would you suggest using sapply - I'm not saying it's an incorrect suggestion, but a reason would be nice.

Duna Over a year ago

I used summary(g[1,]) to extract the value of the integral since g is a list. The use of sapply makes sense because it calls for a specified function (h in this case) for each element in a vector y.

James · Accepted Answer · 2013-11-11 12:53:15Z

1

You need to use [[ to subset h rather than [. This is because [ will return a sub-list rather than the contents. Also integrate returns a complex structure, if you just want the value, append with $value to pick that out.

f = function(n){
  h = list()
  g = numeric()
  y = rexp(n)
  for(i in 1:n){
    h[[i]] = function(x){(x * dexp(x) * (y[i] > 0.5*x))}
    g[i] = integrate(h[[i]], lower=-Inf, upper=Inf)$value
  }
  return(summary(g))
}

f(3)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.2456  0.3269  0.4082  0.4069  0.4876  0.5669

answered Nov 11, 2013 at 12:53

James

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1 Comment

Duna Over a year ago

This is exactly what I wanted to do. sapply also does a similar job as @Thilo suggests.

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