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stats::betaCDF

Cumulative distribution function of the beta distribution

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

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

Description

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

.

of the beta distribution with shape parameters a > 0, b > 0.

The procedure f := stats::betaCDF(a, b) 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 can be converted to a real floating-point number and a and b can be converted to positive floating-point numbers, then the return value f(x) is a floating-point number.

• For numerical values x ≤ 0 and x ≥ 1, the floating-point numbers 0.0, respectively 1.0, are returned even if a and b are symbolic quantities.

• The call f(- infinity ) returns 0.0; the call f( infinity ) return 1.0.

• In all other cases, f(x) returns the symbolic call stats::betaCDF(a, b)(x).

Numerical values of a and b are only accepted if they are 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 = 5 and b = 7 at various points:

```f := stats::betaCDF(5, 7):
f(-infinity), f(-PI), f(1/sqrt(10)), f(0.75), f(1), f(infinity)```

Nonpositive numerical values of a or b lead to an error:

`stats::betaCDF(-5, 7)(0.75)`
```Error: The first shape parameter must be positive. [stats::betaCDF]
```
```Error:
the first shape parameter must be positive [stats::betaCDF] ```
`delete f:`

Example 2

For symbolic arguments, symbolic calls of stats::betaCDF are returned, unless x ≤ 0 or x ≥ 1 can be decided:

```f := stats::betaCDF(a, b):
f(-2), f(0), f(1/3), f(0.4), f(1), f(PI), f(x)```

When positive real numbers are assigned to a and b, the call f(x) returns a floating-point number if x is numerical:

```a := 2: b := PI:
f(-2), f(1/3), f(0.4),  f(PI)```

`delete f, a, b:`

Parameters

 a, b The shape parameters of the beta distribution: arithmetical expressions representing positive real values.