# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# `stats`::`cauchyCDF`

Cumulative distribution function of the Cauchy distribution

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

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

## Description

`stats::cauchyCDF(a, b)` returns a procedure representing the cumulative distribution function

of the Cauchy distribution with median a and scale parameter b > 0.

The procedure `f := stats::cauchyCDF(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 or a symbolic expression:

• If `x` is a floating-point number and `a` and `b` can be converted to suitable floating-point numbers, then `f(x)` returns a floating-point number.

• In all other cases, the symbolic expression ```arctan((x - a)/b)/PI + 1/2``` is returned.

Numerical values of `a` and `b` are only accepted if they are real and `b` 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 cumulative distribution function with a = 2 and at various points:

```f := stats::cauchyCDF(2, 3/4): f(-infinity), f(-10), f(0.8), f(2), f(10.0^4), f(infinity)```

`delete f, x:`

### Example 2

We use symbolic arguments:

```f := stats::cauchyCDF(a, b): f(x), f(sqrt(2)), f(0.9)```

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

```a := PI: b := 1/8: f(sqrt(2)), f(0.9)```

## Parameters

 `a` The median: an arithmetical expression representing a real value `b` The scale parameter: an arithmetical expression representing a positive real value