WEIBULL

WEIBULL(x, shape, scale, cumulative)

Calculates the Weibull distribution probability density (PDF) or cumulative distribution (CDF).

WEIBULL evaluates either the probability density function (PDF) or the cumulative distribution function (CDF) of the Weibull distribution for the given input(s).

Parameters:

• x (Operand) – The input value(s) at which to evaluate the distribution. Must be ≥ 0.

• shape (Operand) –

  The shape parameter α (must be > 0). Determines the distribution shape:

  • α < 1: Decreasing failure rate

  • α = 1: Exponential distribution

  • α > 1: Increasing failure rate

• scale (Operand) – The scale parameter β (must be > 0). Characteristic life parameter.

• cumulative (Operand) –

  Boolean flag (or numeric 0/1) to determine calculation type:

  • False / 0: PDF

  • True / 1: CDF

Return type:

Formula

Returns:

A formula object evaluating to the Weibull distribution value(s).

• Returns DECIMAL if all inputs are scalar

• Returns DECIMAL_ARRAY if any input is an array

Raises:

• ValueError – If x, shape, or scale are not numeric types

• ValueError – If cumulative is not boolean-compatible

Examples

Probability density function (PDF):

WEIBULL(2, 1.5, 3, False)
# Returns the PDF at x=2

Cumulative distribution function (CDF):

WEIBULL(2, 1.5, 3, True)
# Returns the CDF at x=2

Array inputs:

WEIBULL([1, 2, 3], 1.5, 3, True)
# Returns an array of CDF values at x=1,2,3

``x`` — accepted types

• DECIMAL

• DECIMAL_ARRAY

• INTEGER

• INTEGER_ARRAY

``arg_2`` — accepted types

• DECIMAL

• DECIMAL_ARRAY

• INTEGER

• INTEGER_ARRAY

``arg_3`` — accepted types

• DECIMAL

• DECIMAL_ARRAY

• INTEGER

• INTEGER_ARRAY

``cumulative`` — accepted types

• BOOLEAN

• BOOLEAN_ARRAY

• DECIMAL

• DECIMAL_ARRAY

• INTEGER

• INTEGER_ARRAY

Return types

• DECIMAL

• DECIMAL_ARRAY