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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