WEIBULLINV

Updated 2024-03-13 14:34:15.497000

Syntax

SELECT [westclintech].[wct].[WEIBULLINV] (
  <@P, float,>
 ,<@Alpha, float,>
 ,<@Beta, float,>)

Description

Use the scalar function WEIBULLINV to calculate the inverse of the cumulative distribution function of the Weibull distribution.

The formula for the cumulative distribution function is:

F(x;k,b) = 1 - e^{-bx^k}

Arguments

@P

is the cumulative distribution function. @P is an expression of type float or of a type that implicitly converts to float.

@Beta

is the scale parameter of the distribution. @Beta is an expression of type float or of a type that implicitly converts to float.

@Alpha

is the shape parameter of the distribution. @Alpha is an expression of type float or of a type that implicitly converts to float.

Return Type

float

Remarks

@P must be greater than zero and less than one (0 < @P < 1).

@Alpha must be greater than zero (0 < @Alpha).

@Beta must be greater than zero (0 < Beta).

Examples

Calculate the cumulative distribution function:

SELECT wct.WEIBULL(6, 1, 10, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.451188363905974"}]}

Calculate the inverse:

SELECT wct.WEIBULLINV(0.451188363905974, 1, 10);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"6.00000000000001"}]}