Probability density function of Fisher's fdistribution (fratio distribution)
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stats::fPDF(a
, b
)
stats::fPDF(a, b)
returns a procedure representing
the probability density function
of Fisher's fdistribution with shape parameters a > 0, b > 0.
The procedure f:=stats::fPDF(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 ≤ 0 can
be decided, then f(x)
returns 0 If x >
0 can be decided, then f(x)
returns
the value
.
If x is a floatingpoint number and both a and b can be converted to positive floatingpoint numbers, then these values are returned as floatingpoint numbers. Otherwise, symbolic expressions are returned.
The function f
reacts to properties of identifiers
set via assume
.
If x is
a symbolic expression with the property x ≤
0 or x ≥
0, the corresponding values are returned.
f( infinity )
and f( infinity )
return 0.
f(x)
returns the symbolic call stats::fPDF(a,
b)(x)
if neither x ≤
0 nor x >
0 can be decided.
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 probability density function with a = 2 and b = 4 at various points:
f := stats::fPDF(2, 4): f(infinity), f(PI), f(1/2), f(0.5), 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::fPDF(a, b): f(x)
With suitable properties, it can be decided whether x ≥ 0 holds. An explicit expression is returned:
assume(0 <= x): f(x)
unassume(x): delete f:
We use symbolic arguments:
f := stats::fPDF(a, b): f(x)
When numerical values are assigned to a
and b
,
the function f
starts to produce numerical values:
a := 2: b := 1: f(3), f(3.0)
delete f, a, b:

The shape parameters: arithmetical expressions representing positive real values 