[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:


  Any thoughts?  Should I report this on the bug list?

A more general illustration:

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}
Qbeta <- Vectorize(Qbeta0,c("t","shape1","shape2"))

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