Calculate a quantile from a distribution function
cdf2quantile.Rd
Numerically calculate a quantile from a distribution function.
Arguments
- p
a number in the interval (0,1).
- cdf
cumulative distribution function, a function.
- interval
interval in which to look for the root, see Details.
- lower
lower end point of the interval.
- upper
upper end point of the interval.
- ...
any further arguments to be passed to the root finding function and the cdf, see Details.
Details
The quantile, \(q\), is computed numerically as the solution of the equation \(cdf(q)-p=0\).
Function uniroot
is used to find the root. To request higher
precision, set argument tol
. Other arguments in ...
are
passed on to cdf
.
uniroot
needs an interval where to look for the root.
There is a default one, which is extended automatically if it does not
contain the quantile. This assumes that argument cdf
is an
increasing function (as it should be).
To override the default interval, use argument interval
(a
vector of two numbers) or lower
and/or upper
. This may
be necessary if the support of the distribution is not the whole real
line and cdf
does not cope with values outside the support of
the distribution.
Examples
cdf2quantile(0.95, pnorm)
#> [1] 1.644851
cdf2quantile(0.05, pexp) # support [0,Inf) is no problem for
#> [1] 0.05129361
cdf2quantile(0.05, plnorm) # for built-in distributions.
#> [1] 0.1930405
## default predicision is about 4 digits after decimal point
cdf2quantile(0.95, pnorm, mean = 3, sd = 1)
#> [1] 4.644829
cdf2quantile(0.05, pnorm, mean = 3, sd = 1)
#> [1] 1.355143
qnorm(c(0.95, 0.05), mean = 3, sd = 1)
#> [1] 4.644854 1.355146
## request a higher precision:
cdf2quantile(0.05, pnorm, mean = 3, sd = 1, tol = 1e-8)
#> [1] 1.355146
cdf2quantile(0.05, pnorm, mean = 3, sd = 1, tol = 1e-12)
#> [1] 1.355146
## see also examples for plotpdf()