Documentation

# qfuncinv

Inverse Q function

## Syntax

```y = qfuncinv(x) ```

## Description

`y = qfuncinv(x)` returns the argument of the Q function at which the Q function's value is `x`. The input `x` must be a real array with elements between 0 and 1, inclusive.

For a scalar `x`, the Q function is one minus the cumulative distribution function of the standardized normal random variable, evaluated at `x`. The Q function is defined as

`$Q\left(x\right)=\frac{1}{\sqrt{2\pi }}\underset{x}{\overset{\infty }{\int }}\mathrm{exp}\left(-{t}^{2}/2\right)dt$`

The Q function is related to the complementary error function, erfc, according to

`$Q\left(x\right)=\frac{1}{2}\text{erfc}\left(\frac{x}{\sqrt{2}}\right)$`

## Examples

The example below illustrates the inverse relationship between `qfunc` and `qfuncinv`.

```x1 = [0 1 2; 3 4 5]; y1 = qfuncinv(qfunc(x1)) % Invert qfunc to recover x1. x2 = 0:.2:1; y2 = qfunc(qfuncinv(x2)) % Invert qfuncinv to recover x2.```

The output is below.

```y1 = 0 1 2 3 4 5 y2 = 0 0.2000 0.4000 0.6000 0.8000 1.0000 ```