Cumulative distribution function of Fisher's fdistribution (fratio distribution)
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stats::fCDF(a
, b
)
stats::fCDF(a, b)
returns a procedure representing
the cumulative distribution function
of Fisher's fdistribution with shape parameters a > 0, b > 0.
The procedure f:=stats::fCDF(a, b)
can be
called in the form f(x)
with an arithmetical expression x
.
The return value of f(x)
is either a floatingpoint
number or a symbolic expression:
If x
can be converted to a real floating
point number and the shape parameters can be converted to positive
floatingpoint numbers, then f(x)
returns a floating
point number between 0.0 and 1.0.
For all values of a
and b
,
the call f(x)
returns 0.0
if x
is
a nonpositive numerical value or a symbolic expression with the propertyx ≤
0.
The call f( infinity )
returns 0.0.
The call f( infinity )
returns 1.0.
In all other cases, f(x)
returns the symbolic
call stats::fCDF(a, b)(x)
.
Numerical values for 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. It reacts to properties
of identifiers set via assume
.
We evaluate the cumulative distribution function with a = 2 and b = 1 at various points:
f := stats::fCDF(2, 1): f(infinity), f(3), f(0.5), f(2/3), f(PI), f(infinity)
delete f:
If x
is a symbolic object without properties,
then it cannot be decided whether x ≤
0 holds. A symbolic function call is returned:
f := stats::fCDF(a, b): f(x)
With suitable properties, it can be decided whether x ≤ 0 holds. The value 0.0 is returned:
assume(x <= 0): f(x)
MuPAD^{®} does not provide a special function to represent the cumulative distribution function for positive arguments. A symbolic call is returned:
assume(x > 0): f(x)
unassume(x): delete f:
We use symbolic arguments:
f := stats::fCDF(a, b): f(x), f(2)
When numerical values are assigned to a
and b
,
the function f
starts to produce floatingpoint
numbers for numerical arguments:
a := 2: b := 1: f(2)
delete f, a, b:

The shape parameters: arithmetical expressions representing positive real values 