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`stats`::`betaPDF`

Probability density function of the beta distribution

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Syntax

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

Description

`stats::betaPDF(a, b)` returns a procedure representing the probability density function

.

of the beta distribution with shape parameters a > 0 and b > 0

The procedure `f := stats::betaPDF(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` is a real floating-point number and `a` and `b` can be converted to positive floating-point numbers, then `f(x)` returns a floating-point number.

• If 0 < x < 1 can be decided, the expression ```x^(a-1)*(1-x)^(b-1)/beta(a, b)``` is returned. If x ≤ 0 or x ≥ 1 can be decided, then `0`, respectively `0.0`, is returned.

• The calls `f(- infinity )` and ```f( infinity )``` return 0.

• In all other cases, `f(x)` returns the symbolic call `stats::betaPDF(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. The procedure returned by `stats::betaPDF` reacts to properties of its argument.

Examples

Example 1

We evaluate the probability density function with a = 3 and b = 4 at various points:

```f := stats::betaPDF(3, 4): f(-infinity), f(-1), f(1/2), f(0.7), f(infinity)```

`delete f:`

Example 2

If `x` is a symbolic object without properties, then it cannot be decided whether 0 < x < 1 holds. A symbolic function call is returned:

`f := stats::betaPDF(a, b): f(x)`

With suitable properties, an explicit expression is returned:

`assume(0 < x < 1): f(x)`

`assume(x > 1): f(x)`

`unassume(x): delete f:`

Parameters

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

Return Values

Mathematical Modeling with Symbolic Math Toolbox

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