WEIBULL

Updated 2024-03-13 14:33:37.143000

Syntax

SELECT [westclintech].[wct].[WEIBULL] (
  <@X, float,>
 ,<@Alpha, float,>
 ,<@Beta, float,>
 ,<@Cumulative, bit,>)

Description

Use WEIBULL to calculate the Weibull distribution. The formula for the probability density function (pdf) is:

f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^{k}}, & x\geq0 ,\\ 0, & x<0, \end{cases}

Where

{
    "columns": [
        {
            "field": "column 1",
            "maxWidth": 100
        },
        {
            "field": "column 2",
            "maxWidth": 325
        }
    ],
    "rows": [
        {
            "column 1": "x",
            "column 2": "is the value at which to evaluate the function"
        },
        {
            "column 1": "k",
            "column 2": "us the shape parameter"
        },
        {
            "column 1": "λ",
            "column 2": "is the scale parameter"
        }
    ]
}

The formula for the cumulative distribution function (cdf) is:

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

Arguments

@Cumulative

is a logical value that determines if the probability density function (False, 0) or the cumulative distribution function (True, 1) is being calculated.

@X

is the value at which to evaluate the function. @X is an expression of type float or of a type that can be implicitly converted to float.

@Alpha

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

@Beta

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

Return Type

float

Remarks

If @X < 0, WEIBULL returns an error.

If @Alpha = 0 or @Beta = 0, WEIBULL returns an error.

WEIBULL(@X,1,@Beta,@Cumulative)= EXPONDIST(@X,1/@Beta, @Cumulative).

Examples

select wct.WEIBULL(105, 20, 100, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.929581390069277"}]}

select wct.WEIBULL(105, 20, 100, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0355888640245043"}]}

select wct.WEIBULL(6, 1, 10, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0548811636094027"}]}

select wct.EXPONDIST(6, 1.0000 / 10, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0548811636094026"}]}