HypGeomDist ( sampleSuccesses ; sampleSize ; populationSuccesses ; ... )

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Michael Horak - Show more from this author
*COMMENT Visual Realisation

Sample input:

HypGeomDist ( 1 ; 4 ; 8 ; 20 ; 0 )
HypGeomDist ( 1 ; 4 ; 8 ; 20 ; 1 )

Sample output:

0.3632610939112487
0.4654282765737874

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/*
HypGeomDist function

Author
*COMMENT Visual Realisation

Format
HypGeomDist ( sampleSuccesses ; sampleSize ; populationSuccesses ; populationSize ; cumulative )

Parameters
sampleSuccesses - any numeric expression or field containing a non-negative numeric expression
sampleSize - any numeric expression or field containing a non-negative numeric expression
populationSuccesses - any numeric expression or field containing a non-negative numeric expression
populationSize - any numeric expression or field containing a non-negative numeric expression
cumulative - 0 or False, 1 or True

Data type returned
number

Description
Returns the hypergeometric probability distribution of obtaining the number of successes in a sample, based on the success rate of the general population. Given the overall failure rate of a production line, HypGeomDist can calculate the probability of 3 items being defective in a shipment containing 100 items.

Depending on the cumulative parameter, the HypGeomDist function returns either the individual probability of obtaining exactly the number of successes, or the cumulative probability of obtaining at most the number of successes.

The HypGeomDist function parameters are:
sampleSuccesses - the number of successes in the sample;
sampleSize - the size of the sample;
populationSuccesses - the number of successes in the population;
populationSize - the size of the population ;
cumulative - a logical value that determines the form of the function: if cumulative is TRUE, HypGeomDist returns the cumulative probability of obtaining at most the number of successes; if FALSE, it returns the probability of obtaining exactly the number of successes.

February 2, 2006
*/

Let ( [
discrete = Combination ( populationSuccesses ; sampleSuccesses ) * Combination ( populationSize - populationSuccesses ; sampleSize - sampleSuccesses ) / Combination ( populationSize ; sampleSize )
] ;
Case ( 
sampleSuccesses and cumulative ;
discrete + HypGeomDist ( sampleSuccesses - 1 ; sampleSize ; populationSuccesses ; populationSize ; 1 ) ;
discrete )
)

Returns the hypergeometric probability distribution of obtaining the number of successes in a sample, based on the success rate of the general population. Given the overall failure rate of a production line, HypGeomDist can calculate the probability of 3 items being defective in a shipment containing 100 items.

Depending on the cumulative parameter, the HypGeomDist function returns either the individual probability of obtaining exactly the number of successes, or the cumulative probability of obtaining at most the number of successes.

The HypGeomDist function parameters are:
sampleSuccesses - the number of successes in the sample;
sampleSize - the size of the sample;
populationSuccesses - the number of successes in the population;
populationSize - the size of the population ;
cumulative - a logical value that determines the form of the function: if cumulative is TRUE, HypGeomDist returns the cumulative probability of obtaining at most the number of successes; if FALSE, it returns the probability of obtaining exactly the number of successes.

Example:
A box of chocolates contains 20 pieces. Eight pieces contain a hazelnut. If a person selects 4 pieces at random, the probability of exactly 1 piece containing a hazelnut is:
HypGeomDist ( 1 ; 4 ; 8 ; 20 ; 0 ) = 36.33%

The probability of 1 piece or less containing a hazelnut is:
HypGeomDist ( 1 ; 4 ; 8 ; 20 ; 1 ) = 46.54%

Comments

Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

HypGeomDist ( sampleSuccesses ; sampleSize ; populationSuccesses ; ... )

Comments

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