﻿

Accelerating the pace of engineering and science

• 評価版
• 製品アップデート

# stats::fQuantile

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

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

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

## Description

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 floating-point 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 floating-point numbers, then f(x) returns a positive floating-point 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.

## Environment Interactions

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.

## Examples

### Example 1

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:`

### Example 2

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 floating-point 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:`

## Parameters

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