# Documentation

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# `stats`::`fQuantile`

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

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## 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: Argument x must be between 0 and 1. [f] ```
`delete f, a, b:`

## Parameters

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