"Drawings since hit tables in lotteries" and a new multivariate geometric distribution

Norbert Henze

Statistics & Probability Letters, 1998, vol. 40, issue 4, 321-327

Abstract: In number lotteries people choose r numbers out of s. Weekly published "drawings since hit tables" indicate how many drawings have taken place since each of the s numbers was last selected as a winning number. Among many lotto players, they enhance the widespread belief that numbers should be "due" if they have not come up for a long time. Under the assumptions of independence of the drawings and equiprobability of all possible combinations, the random s-vectors Yn, n [greater-or-equal, slanted] 1, of entries in a drawings since hit table after n drawings form a Markov chain. The limit distribution of Yn as n --> [infinity] is a new multivariate generalization of the geometric distribution. The determination of the distribution of the maximum entry in a drawings since hit table within the first n draws of a lottery seems to be an open problem.

Keywords: Lottery; Drawings; since; hit; table; Multivariate; geometric; distribution; Markov; chain (search for similar items in EconPapers)
Date: 1998
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