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 floatingpoint number or a symbolic expression:
If x
is a real floatingpoint number
and a
and b
can be converted
to positive floatingpoint numbers, then f(x)
returns
a floatingpoint number.
If 0 < x <
1 can be decided, the expression x^(a1)*(1x)^(b1)/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.
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.
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:
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:

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