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XLeratorDB/statistics Documentation

SQL Server EXPON.DIST function


 
Updated: 9 August 2010

Use EXPONDIST to calculate an exponential distribution that is equivalent to the function used in EXCEL. Exponential distributions describe times between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate.
 
The equation for the probability density function is:
 EXPONDIST
The equation for the cumulative distribution function is:
EXPONDIST
Syntax
SELECT [wctStatistics].[wct].[EXPONDIST] (
   <@X, float,>
 ,<@Lambda, float,>
 ,<@Cumulative, bit,>)
Arguments
@X
is the value of the function. @X is an expression of type float or of a type that can be implicitly converted to float
@Lambda
is the parameter value. @Lambda is an expression of type float or of a type that can be implicitly converted to float
@Cumulative
is a logical value that determines the probability density function (False, 0) or the cumulative distribution function (True, 1) is being calculated.
Return Types
float
Remarks
·         If @X < 0, EXPONDIST returns an error.
·         If @Lambda ≤ 0, EXPONDIST returns an error
·         EXPONDIST = GAMMADIST(@X,1,1/@Lambda, @Cumulative)
·         EXPONDIST = WEIBULL(@X,1,1/@Lambda, @Cumulative)
Examples

select
wct.EXPONDIST(0.5, 9.5, 'False')
 

This produces the following result

----------------------
0.082191104429646
 
(1 row(s) affected)
 

select
wct.GAMMADIST(0.5,1,1.0000000/9.50000000, 'False')
 

This produces the following result

----------------------
0.0821911044296461
 

select
wct.EXPONDIST(0.5, 9.5, 'True')
 

This produces the following result

----------------------
0.991348304796879
 
(1 row(s) affected)
 

select
wct.GAMMADIST(0.5,1,1.0000000/9.50000000, 'True')
 

This produces the following result

----------------------
0.991348304796879
 
(1 row(s) affected)


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