POISSONINV

Updated 2024-03-13 13:21:11.440000

Syntax

SELECT [westclintech].[wct].[POISSONINV] (
  <@P, float,>
 ,<@Mean, float,>)

Description

Use the scalar function POISSONINV to calculate the inverse of the cumulative distribution function of the Poisson distribution.

The formula for the cumulative distribution function is:

F(k; \lambda) =Q(\lfloor{k+1}\rfloor,\lambda)

Arguments

@P

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

@Mean

is the mean of the distribution. @Mean 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).

@Mean must be greater than or equal to zero (0 = @Mean).

Examples

Calculate the cumulative distribution function:

SELECT wct.POISSON(2, 5, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.124652019483081"}]}

Calculate the inverse:

SELECT wct.POISSONINV(0.124652019483081, 5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"2"}]}