WEIBULL

WEIBULL(x, shape, scale, cumulative)[source]

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.

Supported types:
- INTEGER
- DECIMAL
- INTEGER_ARRAY
- DECIMAL_ARRAY
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
Supported types:
- INTEGER
- DECIMAL
- INTEGER_ARRAY
- DECIMAL_ARRAY
scale (Operand) –
The scale parameter β (must be > 0). Characteristic life parameter.

Supported types:
- INTEGER
- DECIMAL
- INTEGER_ARRAY
- DECIMAL_ARRAY
cumulative (Operand) –
Boolean flag (or numeric 0/1) to determine calculation type:
- False / 0: PDF
- True / 1: CDF
Supported types:
- BOOLEAN
- BOOLEAN_ARRAY

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

Supported types:

DECIMAL
DECIMAL_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