# stats::betaQuantile

Quantile function of the beta distribution

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

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

## Description

`stats::betaQuantile(a, b)` returns a procedure representing the quantile function (inverse) of the cumulative distribution function `stats::betaCDF(a, b)`. For 0 ≤ x ≤ 1, the solution of stats::betaCDF(a, b)(y) = x is given by y = stats::betaQuantile(a, b)(x).

The procedure `f := stats::betaQuantile(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 `a` and `b` can be converted to positive floating-point numbers and `x` is a real number between 0 and 1, then the return value `f(x)` is a floating-point number between 0.0 and 1.0 approximating the real solution y of stats::betaCDF(a, b)(y) = x.

• `f(0)`, `f(0.0)`, `f(1)`, and `f(1.0)` produce 0, 0.0, 1, and 1.0, respectively, for all values of `a` and `b`.

• In all other cases, `f(x)` returns the symbolic call `stats::betaQuantile(a, b)(x)`.

Numerical values of `a` and `b` are only accepted if they are positive.

## Environment Interactions

The function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

We evaluate the quantile function with a = π and b = 11 at the point :

`f := stats::betaQuantile(PI, 11): f(9/10)`

The value `f(x)` satisfies ```stats::betaCDF(PI, 11)(f(x)) = x```:

`stats::betaCDF(PI, 11)(f(0.98765))`

`delete f:`

### Example 2

For symbolic arguments, symbolic calls are returned:

`f := stats::betaQuantile(a, b): f(x), f(0.9)`

If `a`, `b` evaluate to real numbers and `x` to a real number between 0 and 1, then the call `f(x)` produces a float:

`a := 17: b := 6: f(0.9)`

Numerical values for x are only accepted if 0 ≤ x ≤ 1:

`f(2)`
```Error: An argument x with 0 <= x <= 1 is expected. [f] ```
`delete f, a, b:`

## Parameters

 `a`, `b` The shape parameters of the beta distribution: arithmetical expressions representing positive real values.