Updated: 9 August 2010

Use BINOMDIST to calculate the binomial distribution. The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. The formula for the probability density function is:

The cumulative distribution function is:

SELECT [wctStatistics].[wct].[BINOMDIST] (

<@Number_s, float,>

,<@Trials, float,>

,<@Probability_s, float,>

,<@Cumulative, bit,>)

is the number of successes in trials. @*Number_s *is an expression of type **float** or of a type that can be implicitly converted to **float**.

is the number of independent trials. @*Trials *is an expression of type **float** or of a type that can be implicitly converted to **float**.

is the probability of success in each trail. @*Probability_s *is an expression of type **float** or of a type that can be implicitly converted to **float**.

is a logical value that determines the probability density function (False, 0) or the cumulative distribution function (True, 1) is being calculated.

float

· *@Number_s* and *@Trials *are truncated to zero decimal places.

· If @*Number_s*, *@Trials*, or *@Probability_s* <0, BINOMDIST returns an error.

· If *@Number_s* > *@Trials*, BINOMDIST returns an error.

· If *@Probability_s* > 1, BINOMDIST returns an error.

· If *@Cumulative* = False then BINOMDIST =

BICO*(@Trials,@trials*-@*number_s*)*POWER(*@Probability_s*,*@Number_s*)*POWER((1-*@Probability_s*),(*@Trials*-*@Number_s*))

· If @Cumulative = True then BINOMDIST =

1-BETADIST(*@Probability_s*, *@Number_s*+1, *@Trials*-*@Number_s*, NULL, NULL)

select wct.BINOMDIST(6,10,.5,'False')

This produces the following result

----------------------

0.205078125000001

(1 row(s) affected)

select wct.BINOMDIST(6,10,.5,'True')

This produces the following result

----------------------

0.828125

(1 row(s) affected)

select wct.BICO(10, 10-6)

*POWER(.500000000,6.00000000)

*POWER(1.00000000-.500000000,10.0000000-6.0000000)

This produces the following result

----------------------

0.205078125

(1 row(s) affected)

select 1 - wct.betadist(.5,6+1, 10 -6, null,null)

This produces the following result

----------------------

0.828124999999999

(1 row(s) affected)