Estimating Hot Numbers and Testing Uniformity for the Lottery
研究了彩票中不同号码出现概率的估计方法，开发了计算最大似然估计及其方差协方差矩阵的数值方法，并给出了检验号码等概率的广义似然比统计量，应用于美国彩票数据。
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.