CAUCHYINV

Updated 2024-03-07 20:14:56.247000

Syntax

SELECT [westclintech].[wct].[CAUCHYINV] (
  <@P, float,>
 ,<@A, float,>
 ,<@B, float,>)

Description

Use the scalar function CAUCHYINV to calculate the inverse lower cumulative distribution of the CAUCHY distribution.

The formula for the lower cumulative distribution function is:

F(x; x_0,\gamma)=\frac{1}{\pi} \arctan\left(\frac{x-x_0}{\gamma}\right)+\frac{1}{2}

Arguments

@A

is the location parameter. @A is an expression of type float or of a type that implicitly converts to float.

@P

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

@B

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

Return Type

float

Remarks

@B must be greater than zero (B > 0).

@P must be greater than or equal to zero and less than or equal to one (0 ≤ @P ≤ 1).

Examples

Calculate the inverse of the lower cumulative distribution function:

SELECT wct.CAUCHYINV(.75, 0, 1);

This produces the following result.

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