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

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  • Henze, Norbert
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 40 (1998)
    Issue (Month): 4 (November)
    Pages: 321-327

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    Handle: RePEc:eee:stapro:v:40:y:1998:i:4:p:321-327

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    Keywords: Lottery Drawings since hit table Multivariate geometric distribution Markov chain;

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