Generic function to find the quantiles of a distribution, given the equivalent probability distribution function.

## Arguments

- pdist
Probability distribution function, for example,

`pnorm`

for the normal distribution, which must be defined in the current workspace. This should accept and return vectorised parameters and values. It should also return the correct values for the entire real line, for example a positive distribution should have`pdist(x)==0`

for \(x<0\).- p
Vector of probabilities to find the quantiles for.

- special
Vector of character strings naming arguments of the distribution function that should not be vectorised over. Used, for example, for the

`rate`

and`t`

arguments in`qpexp`

.- ...
The remaining arguments define parameters of the distribution

`pdist`

. These MUST be named explicitly.This may also contain the standard arguments

`log.p`

(logical; default`FALSE`

, if`TRUE`

, probabilities p are given as log(p)), and`lower.tail`

(logical; if`TRUE`

(default), probabilities are P[X <= x] otherwise, P[X > x].).If the distribution is bounded above or below, then this should contain arguments

`lbound`

and`ubound`

respectively, and these will be returned if`p`

is 0 or 1 respectively. Defaults to`-Inf`

and`Inf`

respectively.

## Details

This function is intended to enable users to define `"q"`

functions for
new distributions, in cases where the distribution function `pdist`

is
available analytically, but the quantile function is not.

It works by finding the root of the equation \(h(q) = pdist(q) - p = 0\).
Starting from the interval \((-1, 1)\), the interval width is expanded by
50% until \(h()\) is of opposite sign at either end. The root is then
found using `uniroot`

.

This assumes a suitably smooth, continuous distribution.

An identical function is provided in the flexsurv package.