Cumulative distribution function of Fisher's f-distribution (fratio distribution)
This functionality does not run in MATLAB.
stats::fCDF(a, b) returns a procedure representing the cumulative distribution function
of Fisher's f-distribution 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 floating-point 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 floating-point 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.
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)
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 floating-point numbers for numerical arguments:
a := 2: b := 1: f(2)
delete f, a, b:
The shape parameters: arithmetical expressions representing positive real values