# stats::logisticQuantile

Quantile function of the logistic distribution

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::logisticQuantile(`m`, `s`)
```

## Description

`stats::logisticQuantile(m, s)` returns a procedure representing the quantile function (inverse)

of the cumulative distribution function ```stats::logisticCDF(m, s)```. For 0 ≤ x ≤ 1, the solution of `stats::logisticCDF`(m, s)(y) = x is given by

.

The procedure `f := stats::logisticQuantile(m, s)` 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, ±`infinity`, or a symbolic expression:

The call `f(x)` returns a real floating-point number if `x` is a floating-point number between `0.0` and `1.0`, `m` can be converted to a real floating-point number, and `s` can be converted to a positive real floating-point number.

The calls `f(0)` and `f(0.0)` produce ```- infinity```; the calls `f(1)` and `f(1.0)` produce `infinity`.

In all other cases, the symbolic expression `m + sqrt(3)*s*ln(x/(1-x))/PI` is returned.

Numerical values of x are only accepted if 0 ≤ x ≤ 1.

Numerical values of m and s are only accepted if they are real and s is 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 mean `m` = 0 and standard deviation `s` = 1 at various points:

```f := stats::logisticQuantile(0, 1): f(0), f(1/10), f(0.7), f(0.999999999), f(1)```

The value `f(x)` satisfies ```stats::logisticCDF(0, 1)(f(x))``` = `x`:

`stats::logisticCDF(0, 1)(f(0.987654321))`

`delete f:`

### Example 2

We use symbolic arguments:

`f := stats::logisticQuantile(m, s): f(x), f(1/3), f(0.4)`

When suitable numerical values are assigned to `a` and `b`, the function `f` starts to produce numerical values:

`m := 0: s := 1: f(0.999), f(999/1000)`

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, m, s:`

## Parameters

 `m` The mean: an arithmetical expression representing a real value `s` The standard deviation: an arithmetical expression representing a positive real value