Quantile function of Fisher's fdistribution (fratio distribution)
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stats::fQuantile(a
, b
)
stats::fQuantile(a, b)
returns a procedure
representing the quantile function (inverse) of the cumulative distribution
function stats::fCDF(a, b)
. For 0
≤ x ≤ 1, the
solution of stats::fCDF(a, b)(y)
= x is given by y = stats::fQuantile(a, b)(x).
The procedure f:=stats::fQuantile(a, b)
can
be called in the form f(x)
with arithmetical expressions x
.
The return value of f(x)
is either a floatingpoint
number, infinity,
or a symbolic expression:
If x
is a real number between 0 and 1 and a
and b
can
be converted to positive floatingpoint numbers, then f(x)
returns
a positive floatingpoint number approximating the solution y of stats::fCDF(a, b)(y)
= x.
The calls f(0)
and f(0.0)
produce 0.0 for
all values of a
and b
.
The calls f(1)
and f(1.0)
produce infinity for
all values of a
and b
.
In all other cases, f(x)
returns the symbolic
call stats::fQuantile(a, b)(x)
.
Numerical values of x are only accepted if 0 ≤ x ≤ 1.
Numerical values of a
and b
are
only accepted if they are real and positive.
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision. The procedure generated
by stats::fQuantile
is sensitive to properties
of identifiers, which can be set via assume
.
We evaluate the quantile function with a = π and b = 11 at various points:
f := stats::fQuantile(PI, 11): f(0), f(1/10), f(0.5), f(1  10^(10)), f(1)
The value f(x)
satisfies stats::fCDF(π,
11)(f(x)) = x:
stats::fCDF(PI, 11)(f(0.987654321))
delete f:
We use symbolic arguments:
f := stats::fQuantile(a, b): f(x), f(9/10)
When positive real values are assigned to a
and b
,
the function f
starts to produce floatingpoint
values:
a := 17: b := 6: f(0.999), f(1  sqrt(2)/10^5)
Numerical values for x are only accepted if 0 ≤ x ≤ 1:
f(0.5)
f(2)
Error: An argument x with 0 <= x <= 1 is expected. [f]
delete f, a, b:

The shape parameters: arithmetical expressions representing positive real values 