Probability density function of the beta distribution

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stats::betaPDF(a, b)


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.


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:


a, b

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

Return Values