Geometric mean functions returning Inf

Question

Trying to solve a homework problem:

I have two functions to get the geometric mean from 1000 observations from the exponential distribution with a rate of .01. The following keeps returning Inf.

gmean <- function(n)
{
    
  prod(n)^(1/length(n))
  
}

x<-rexp(1000,1/100)
    
    
    gmean(x)

but this does not

gmean1 <- function(n)
{
  
 exp(mean(log(n)))
  
}

x<-rexp(1000,1/100)
gmean1(x)

Why is this? I think it's something to do with the prod function but I'm not sure.

Answer 1

The problem is that when you do prod(n) in your function, it calculates the result of this call before raising it to the power of (1/length(n)). Since the mean of x is about 100, you can expect this call to return a value with a similar order of magnitude to 100^1000, which is much higher than the maximum number that R will return (R will call anything above around 10^308 Inf).

Any mathematical operation you attempt on Inf will also return Inf, so your naive implementation will not work if x is greater than about 154:

100^154
#> [1] 1e+308

100^155
#> [1] Inf

In actuality, because the majority of numbers are less than 100 in your sample, you might get to an x length of about 180 before you started generating Inf

In any case, it would be safer to stick to

gmean <- function(n) exp(sum(log(n))/length(n))