RandomWeightedRank ( total )

Returns a random integer between 1 and total such that the probability of each number is proportional to itself.

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Jeremy Bante

https://github.com/jbante/

Sample input:

List (
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 );
RandomWeightedRank ( 10 )
)

Sample output:

6
9
7
10
10
9
3
6
7
5

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

/**
 * =====================================
 * RandomWeightedRank ( total )
 *
 * PURPOSE:
 *		Returns a random integer between 1 and total such that the probability
 *		of each number is proportional to itself. For example, 2 is twice as
 *		likely as 1, and 3 is 3 times as likely as 1. This may be useful for
 *		ordinally weighted lotteries, where applicants have a number of lottery
 *		tickets determined by some ranking. For example, you might want to
 *		randomly award a scholarship, but you might also want individuals with
 *		greater financial need to be more likely to receive the scholarship.
 *
 * RETURNS:
 *		A random integer between 1 and total, inclusive.
 *
 * PARAMETERS:
 *		total: The number of items in a list to select from.
 *
 * DEPENDENCIES: none
 *
 * HISTORY:
 *		CREATED on 2012-02-08 by Jeremy Bante <http://scr.im/jbante>.
 * =====================================
 */

Let ( [
	~sampleSpace = total * ( total + 1 ) / 2;	// sum of all ranks
	~random = Ceiling ( Random * ~sampleSpace )	// sample from "lottery"
];
	// find "winning" rank as inverse of sum of ranks formula
	Ceiling (
		( Sqrt ( 8 * ~random + 1 ) - 1 ) / 2
	)
)

Returns a random integer between 1 and total such that the probability of each number is proportional to itself. For example, 2 is twice as likely as 1, and 3 is 3 times as likely as 1. This may be useful for ordinally weighted lotteries, where applicants have a number of lottery tickets determined by some ranking. For example, you might want to randomly award a scholarship, but you might also want individuals with greater financial need to be more likely to receive the scholarship.

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

RandomWeightedRank ( total )

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