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stats::fCDF

Cumulative distribution function of Fisher's f-distribution (fratio distribution)

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

```stats::fCDF(a, b)
```

Description

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.

Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision. It reacts to properties of identifiers set via assume.

Examples

Example 1

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:`

Example 2

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:`

Example 3

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:`

Parameters

 a, b The shape parameters: arithmetical expressions representing positive real values