Generic function to find the quantiles of a distribution, given the equivalent probability distribution function.
qgeneric(pdist, p, special = NULL, ...)Vector of quantiles of the distribution at p.
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
\(x<0\).
Vector of probabilities to find the quantiles for.
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.
Christopher Jackson <chris.jackson@mrc-bsu.cam.ac.uk>
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.
qnorm(c(0.025, 0.975), 0, 1)
qgeneric(pnorm, c(0.025, 0.975), mean=0, sd=1) # must name the arguments
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