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Journal of the American Statistical Association Volume 88, 1993 - Issue 422
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Theory and Method

Estimating Hot Numbers and Testing Uniformity for the Lottery

Richard Johnson Department of Statistics, University of Wisconsin, Madison, WI, 53706
&
Jerome Klotz Department of Statistics, University of Wisconsin, Madison, WI, 53706
Pages 662-668 | Received 01 Jan 1991, Published online: 27 Feb 2012
 
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Abstract

We consider the problem of estimating probabilities for the different numbers in a lottery when the winning numbers are selected sequentially without replacement. Numerical methods are developed to compute maximum likelihood estimates of the probabilities and their variance-covariance matrix based on observed outcomes. The generalized likelihood ratio statistic –2 ln(λ) for testing equiprobable numbers is also given. The methods are applied to a data set from the Lotto America lottery. The properties of the procedure are studied by simulation.

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