GEOMETRIC

Updated 2024-03-08 16:08:18.577000

Syntax

SELECT [westclintech].[wct].[GEOMETRIC] (
  <@X, float,>
 ,<@P, float,>)

Description

Use the scalar function GEOMETRIC to calculate the probability mass function of the geometric distribution.

The formula for the probability mass function is:

Pr(X=k)=p(1-p)^k

Arguments

@P

is the probability of success. @P is an expression of type float or of a type that implicitly converts to float.

@X

is the number of failures. @X is an expression of type float or of a type that implicitly converts to float.

Return Type

float

Remarks

@X must be greater than or equal to zero (@X ≥ 0).

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

@X is truncated to zero decimal places

For the lower cumulative distribution, use GEOMETRICP.

Examples

Calculate the probability mass function:

SELECT wct.GEOMETRIC(3, 0.4);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0864"}]}

You can use the SeriesInt function from the XLeratorDB/math library to generate a dataset which can be pasted into EXCEL to generate a graph of the probability mass function.

SELECT SeriesValue,

       wct.GEOMETRIC(SeriesValue, 0.1) as [f(x,0.1)],

       wct.GEOMETRIC(SeriesValue, 0.3) as [f(x,0.3)],

       wct.GEOMETRIC(SeriesValue, 0.5) as [f(x,0.5)],

       wct.GEOMETRIC(SeriesValue, 0.7) as [f(x,0.7)],

       wct.GEOMETRIC(SeriesValue, 0.9) as [f(x,0.9)]

FROM wct.SeriesInt(0, 10, NULL, NULL, NULL);

This is an EXCEL-generated graph of the results