BETAI

Updated 2024-03-07 19:47:07.150000

Syntax

SELECT [westclintech].[wct].[BETAI] (
  <@A, float,>
 ,<@B, float,>
 ,<@X, float,>)

Description

Use the scalar function BETAI to calculate the incomplete beta function. The incomplete beta function is defined by:

I_x(a,b)=\frac{\text{B}_x(a,b)}{\text{B}(a,b)}=\frac{1}{\text{B}(a,b)}\int_0^xt^{a-1}(1-t)^{b-1}dt

Arguments

@A

is any real number greater than or equal to zero. @A is an expression of type float or of a type that can be implicitly converted to float. @A is the lower bound to the distribution. If you enter NULL, @A defaults to zero

@B

is any real number greater than or equal to zero. @B is an expression of type float or of a type that can be implicitly converted to float. @B is the upper bound to the distribution. If you enter NULL @B defaults to to zero.

@X

is any real number greater than or equal to zero and less than or equal to one. @X is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @A = 0 or @B = 0, BETAI returns an error.

If @X < 0 or @X > 1, BETAI returns an error.

@X = 0 or @X = 1, BETAI = @X.

BETAI(@A, @B, @X) = BETADIST(@X, @A, @B, 0, 1).

Examples

select wct.BETAI(1, 5, .45);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.9496715625"}]}

select wct.BETADIST(.45, 1, 5, 0, 1);

This produces the following result

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.9496715625"}]}