quantiles on square transformed densities incorrect

[robjhyndman]

library(distributional)
dist_normal()^2 |> hilo()
#> <hilo[1]>
#> [1] [3.841459, 3.841459]95
dist_normal(500,20)^2 |> hilo()
#> Error in `new_hilo()`:
#> ! `upper` can't be lower than `lower`.

^{Created on 2024-10-04 with reprex v2.1.1}

Possibly because transformation is not monotonic over sample space of distribution?

[robjhyndman]

This is the cause of the problem described at https://forum.posit.co/t/fable-and-distributional-packages-hilo-function-error/193716

[mitchelloharawild]

Yes, transformations are assumed monotonic over the support of the distribution.
I can't think of an efficient way to test this yet, currently this test is used:

distributional/R/transformed.R

Lines 165 to 174 in 3a72169

	monotonic_increasing <- function(f, support) {
	# Shortcut for identity function (used widely in ggdist)
	if(!is.primitive(f) && identical(body(f), as.name(names(formals(f))))) {
	return(TRUE)
	}
	# Currently assumes (without checking, #9) monotonicity of f over the domain
	x <- f(field(support, "lim")[[1]])
	isTRUE(x[[2L]] > x[[1L]])
	}

[mitchelloharawild]

Also noting that this is mentioned in the documentation of dist_transformed().

distributional/R/transformed.R

Lines 10 to 11 in 3a72169

	#' @param transform A function used to transform the distribution. This
	#' transformation should be monotonic over appropriate domain.

[mitchelloharawild]

This is now patch fixed, essentially since the domain goes from (-Inf, Inf) to [0, Inf) the monotonicity requirement of dist_transformed() is violated. Of course for most of the density here it isn't a problem, and the error was due to a boundary condition (defaulting monotonic decreasing rather than increasing).

The better solution requires a symbolic understanding of function monotonicity like:

• expr: x^2
• monotonic: {(-Inf, 0), [0, Inf)}