quantile functions: mileage may vary

When experimenting with various quantiles functions in R, I was shocked [ok this is a bit excessive, let us say surprised] by how widely the execution times would vary. To the point of blaming a completely different feature of R. Borrowing from Charlie Geyer’s webpage on the topic of probability distributions in R, here is a table for some standard distributions: I ran

u=runif(1e7)
system.time(x<-qcauchy(u))

choosing an arbitrary parameter whenever needed.

Distribution	Function	Time
Cauchy	qcauchy	2.2
Chi-Square	qchisq	43.8
Exponential	qexp	0.95
F	qf	34.2
Gamma	qgamma	37.2
Logistic	qlogis	1.7
Log Normal	qlnorm	2.2
Normal	qnorm	1.4
Student t	qt	31.7
Uniform	qunif	0.86
Weibull	qweibull	2.9

Of course, it does not mean much in that all the slow distributions (except for Weibull) are parameterised. Nonetheless, that a chi-square inversion take 50 times longer than a uniform inversion remains puzzling as to why it is not coded more efficiently. In particular, I was wondering why the chi-square inversion was slower than the Gamma inversion. Rerunning both inversions showed that they are equivalent:

> u=runif(1e7)
> system.time(x<-qgamma(u,sha=1.5))
utilisateur système écoulé
 21.534 0.016 21.532
> system.time(x<-qchisq(u,df=3))
utilisateur système écoulé
21.372 0.008 21.361

Which also shows how variable system.time can be.