Statistical auditing and randomness test of lotto k / N-type games

H. F. Coronel-Brizio; A. R. Hernández-Montoya; F. Rapallo; E. Scalas

doi:10.1016/j.physa.2008.07.017

Statistical auditing and randomness test of lotto k / N-type games

H. F. Coronel-Brizio
, A. R. Hernández-Montoya
, F. Rapallo
, E. Scalas

Research output: Contribution to journal › Article › peer-review

Abstract

One of the most popular lottery games worldwide is the so-called "lotto k / N". It considers N numbers 1, 2, ..., N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.

Original language	English
Pages (from-to)	6385-6390
Number of pages	6
Journal	Physica A: Statistical Mechanics and its Applications
Volume	387
Issue number	25
DOIs	https://doi.org/10.1016/j.physa.2008.07.017
Publication status	Published - 1 Nov 2008
Externally published	Yes

Keywords

Combinatorial calculus
Empirical randomness test
Lottery games
Multivariate hypothesis testing
Statistical models

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10.1016/j.physa.2008.07.017

Cite this

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title = "Statistical auditing and randomness test of lotto k / N-type games",

abstract = "One of the most popular lottery games worldwide is the so-called {"}lotto k / N{"}. It considers N numbers 1, 2, ..., N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.",

keywords = "Combinatorial calculus, Empirical randomness test, Lottery games, Multivariate hypothesis testing, Statistical models",

author = "Coronel-Brizio, \{H. F.\} and Hern{\'a}ndez-Montoya, \{A. R.\} and F. Rapallo and E. Scalas",

note = "Funding Information: A.R.H.M. was supported by Conacyt-Mexico under sabbatical Grant 75932 and Grant 80720. F.R. and E.S. were supported by local research funds provided by East Piedmont University. ",

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doi = "10.1016/j.physa.2008.07.017",

language = "English",

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AU - Coronel-Brizio, H. F.

AU - Hernández-Montoya, A. R.

AU - Rapallo, F.

AU - Scalas, E.

N1 - Funding Information: A.R.H.M. was supported by Conacyt-Mexico under sabbatical Grant 75932 and Grant 80720. F.R. and E.S. were supported by local research funds provided by East Piedmont University.

PY - 2008/11/1

Y1 - 2008/11/1

N2 - One of the most popular lottery games worldwide is the so-called "lotto k / N". It considers N numbers 1, 2, ..., N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.

AB - One of the most popular lottery games worldwide is the so-called "lotto k / N". It considers N numbers 1, 2, ..., N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.

KW - Combinatorial calculus

KW - Empirical randomness test

KW - Lottery games

KW - Multivariate hypothesis testing

KW - Statistical models

UR - https://www.scopus.com/pages/publications/51049105256

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DO - 10.1016/j.physa.2008.07.017

M3 - Article

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SP - 6385

EP - 6390

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 25

ER -

Statistical auditing and randomness test of lotto k / N-type games

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Keywords

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