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# stats::normalQuantile

Quantile function of the normal distribution

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::normalQuantile(m, v)
```

## Description

stats::normalQuantile(m, v) returns a procedure representing the quantile function (inverse) of the cumulative distribution function stats::normalCDF(m, v) of the normal distribution with mean m and variance v > 0: For 0 ≤ x ≤ 1, the solution of stats::normalCDF(m, v)(y) = x is given by y = stats::normalQuantile(m, v)(x).

The procedure f := stats::normalQuantile(m, v) 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:

If x is a real number between 0 and 1 and both m and v can be converted to floating-point numbers, then f(x) returns a real floating-point number approximating the solution y of stats::normalCDF(m, v)(y) = x.

The calls f(0) and f(0.0) produce -infinity for all values of m and v.

The calls f(1) and f(1.0) produce infinity for all values of m and v.

In all other cases, f(x) returns the symbolic call stats::normalQuantile(m, v)(x).

Numerical values for m and v are only accepted if they are real and v 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 = π and variance v = 11 at various points:

```f := stats::normalQuantile(PI, 11):
f(0), f(1/10), f(0.5), f(1 - 10^(-10)), f(1)```

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

`stats::normalCDF(PI, 11)(f(0.987654))`

`delete f:`

### Example 2

We use symbolic arguments:

`f := stats::normalQuantile(m, v): f(x), f(9/10)`

When numerical values are assigned to m and v, the function f starts to produce floating-point values:

`m := 17: v := 6: f(9/10), f(0.999)`

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, v:`

## Parameters

 m The mean: an arithmetical expression representing a real value v The variance: an arithmetical expression representing a positive real value