Parameterisation of R::dexp

Question

I have just spent a while trying to find a bug in my code which has turned out to be an unusual (at least to me) parameterisation for the R::dexp function. For example:

cppFunction("
  double my_dexp(double x, double lambda, double is_log) {
    return R::dexp(x, lambda, is_log);
  }
")

> my_dexp(4.5, 2.5, FALSE)
[1] 0.06611956
> dexp(4.5, 2.5, FALSE)
[1] 3.251824e-05

Looking here I can see that they use the definition:

double R::dexp(double x, double sl, int lg)

but I haven't been able to find out what sl stands for. I'm not sure if this is documented anywhere - so hopefully this post stands as a warning to others who have used the function like me, and also if anyone can help as to what parameterisation has been used, and why.

Answer 1

If you look at the function definition for dexp,

R> dexp
function (x, rate = 1, log = FALSE) 
.Call(C_dexp, x, 1/rate, log)

you'll see that dexp calls the C function C_dexp with parameter 1/rate. This is what R::dexp is mirroring. In Rcp, they always use the same parameterisation as R itself does at the C level which may be different than the R level.

That means

R> my_dexp(4.5, 1/2.5, FALSE) - dexp(4.5, 2.5, FALSE)
[1] 0

If you look at the Wikipedia page on the exponential function, you'll see the alternative parameterisation based on the reciprocal of the rate parameter, lambda. In this parameterisation, the parameter beta=1/lambda takes the role of a survival parameter. So the expected duration of survival of the system is beta units of time.