stats::weibullPDF

Probability density function of the Weibull distribution

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Syntax

stats::weibullPDF(a, b)

Description

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

of the Weibull distribution with shape parameter a > 0 and scale parameter b > 0.

The procedure f := stats::weibullPDF(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 ≤ 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 both a and b can be converted to positive floating-point numbers, 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(- infinity ) and f( infinity ) return 0.

f(x) returns the symbolic call stats::weibullPDF(a, b)(x) if neither x ≤ 0 nor x > 0 can be decided.

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

Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision. The procedure generated by stats::weibullPDF reacts to properties of identifiers set via assume.

Examples

Example 1

We evulate the probability density function with a = 2 and b = 1 at various points:

f := stats::weibullPDF(2, 1): f(1/5), f(0.5), f(-1), f(x)

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::weibullPDF(a, b): f(x)

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

assume(0 < x): f(x)

unassume(x): delete f:

Example 3

We use symbolic arguments:

f := stats::weibullPDF(a, b): f(x), f(3)

When numerical values are assigned to a and b, the function f starts to produce numerical values:

a := 2: b := 1: f(3), f(3.0)

delete f, a, b:

Parameters

a

The shape parameter: an arithmetical expression representing a positive real value

b

The scale parameter: an arithmetical expression representing a positive real value

Return Values

procedure.