[Rd] unstable corner of parameter space for qbeta?
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Thu Mar 26 02:09:16 CET 2020
I've discovered an infelicity (I guess) in qbeta(): it's not a bug,
since there's a clear warning about lack of convergence of the numerical
algorithm ("full precision may not have been achieved"). I can work
around this, but I'm curious why it happens and whether there's a better
workaround -- it doesn't seem to be in a particularly extreme corner of
parameter space. It happens, e.g., for these parameters:
phi <- 1.1
i <- 0.01
t <- 0.001
shape1 = i/phi ## 0.009090909
shape2 = (1-i)/phi ## 0.9
qbeta(t,shape1,shape2) ## 5.562685e-309
## brute-force uniroot() version, see below
Qbeta0(t,shape1,shape2) ## 0.9262824
The qbeta code is pretty scary to read: the warning "full precision
may not have been achieved" is triggered here:
https://github.com/wch/r-source/blob/f8d4d7d48051860cc695b99db9be9cf439aee743/src/nmath/qbeta.c#L530
Any thoughts? Should I report this on the bug list?
A more general illustration:
http://www.math.mcmaster.ca/bolker/misc/qbeta.png
===
fun <- function(phi,i=0.01,t=0.001, f=qbeta) {
f(t,shape1=i/phi,shape2=(1-i)/phi, lower.tail=FALSE)
}
## brute-force beta quantile function
Qbeta0 <- function(t,shape1,shape2,lower.tail=FALSE) {
fn <- function(x) {pbeta(x,shape1,shape2,lower.tail=lower.tail)-t}
uniroot(fn,interval=c(0,1))$root
}
Qbeta <- Vectorize(Qbeta0,c("t","shape1","shape2"))
curve(fun,from=1,to=4)
curve(fun(x,f=Qbeta),add=TRUE,col=2)
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