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XLeratorDB/statistics Documentation

SQL Server geometric distribution function


GEOMETRICP

Updated: 31 July 2010

Use GEOMETRICP to calculate the cumulative distribution function of the geometric distribution.
 
The formula for the cumulative distribution function is:

GEOMETRICP function for SQL Server
 
Syntax
SELECT [wctStatistics].[wct].[GEOMETRICP] (
  <@X, float,>
 ,<@P, float,>)
Arguments
@X
is the number of failures. @X is an expression of type float or of a type that implicitly converts to float
@P
is the probability of success. @P is an expression of type float or of a type that implicitly converts to float
Return Types
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).
·         For the probability mass function, use GEOMETRIC.
·         For the upper cumulative distribution use 1 – GEOMTRICP(@X-1, @P).
Examples
Calculate the cumulative distribution function:
SELECT wct.GEOMETRICP(3,0.4)
This produces the following result
----------------------
0.8704
 
(1 row(s) affected)

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 cumulative distribution function.
SELECT SeriesValue
,wct.GEOMETRICP(SeriesValue, 0.1) as [f(x,0.1)]
,wct.GEOMETRICP(SeriesValue, 0.3) as [f(x,0.3)]
,wct.GEOMETRICP(SeriesValue, 0.5) as [f(x,0.5)]
,wct.GEOMETRICP(SeriesValue, 0.7) as [f(x,0.7)]
,wct.GEOMETRICP(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




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