Estimating Hot Numbers and Testing Uniformity for the Lottery
作者:
Richard Johnson,
Jerome Klotz,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1993)
卷期:
Volume 88,
issue 422
页码: 662-668
ISSN:0162-1459
年代: 1993
DOI:10.1080/01621459.1993.10476320
出版商: Taylor & Francis Group
关键词: Likelihood ratio test;Maximum likelihood estimators;Sampling without replacement
数据来源: Taylor
摘要:
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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