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# stats::chisquareCDF

Cumulative distribution function of the chi-square distribution

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::chisquareCDF(m)
```

## Description

stats::chisquareCDF(m) returns a procedure representing the cumulative distribution function

of the chi-square distribution with mean m > 0.

The procedure f := stats::chisquareCDF(m) 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 x ≤ 0 can be decided, then f(x) returns 0. If x > 0 can be decided, then f(x) returns the value .

If x is a floating-point number and m can be converted to a positive floating-point number, then these values are returned as floating-point numbers. Otherwise, symbolic expressions are returned.

The function f reacts to properties of identifiers set via assume. If x is a symbolic expression with the property x ≤ 0 or x ≥ 0, the corresponding values are returned.

f(x) returns the symbolic call stats::chisquareCDF(m)(x)if neither x ≤ 0 nor x > 0 can be decided.

Numerical values for m are only accepted if they are real and positive.

Note that, for large m, exact results may be costly to compute. If floating-point values are desired, it is recommended to pass floating-point arguments x to f rather than to compute exact results f(x) and convert them via float. Cf. Example 4.

## 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 mean m = 2 at various points:

```f := stats::chisquareCDF(2):
f(-infinity), f(-3), f(1/2), f(0.5), f(PI), f(infinity)```

`delete f:`

### Example 2

If x is a symbolic object without properties, then it cannot be decided whether x ≥ 0 holds. A symbolic function call is returned:

```f := stats::chisquareCDF(m):
f(x)```

With suitable properties, it can be decided whether x ≥ 0 holds. An explicit expression is returned:

```assume(0 <= x):
f(x)```

For integer values of m, the special function igamma can be expressed in terms of more elementary functions:

```m := 6:
f(x)```

```m := 5:
f(x)```

`unassume(x): delete f, m:`

### Example 3

We use a symbolic mean m:

```f := stats::chisquareCDF(m):
f(3), f(3.0)```

When a numerical value is assigned to m, the function f starts to produce numerical values:

```m := PI:
f(3), f(3.0)```

`delete f, m:`

### Example 4

We consider a chi-square distribution with large mean m = 1000:

`f := stats::chisquareCDF(1000):`

For floating-point approximations, one should not compute an exact result and convert it via float. For large mean m, it is faster to pass a floating-point argument to f. The following call takes some time, because an exact computation of the huge integer gamma(m/2) = gamma(500) = 499! is involved:

`float(f(1023))`

The following call is much faster:

`f(float(1023))`

`delete f:`

## Parameters

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

## See Also

### MuPAD Functions

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