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非平稳泊松过程强度函数的贝叶斯线性估计AI 解读

A Bayesian approach is taken to the problem of estimating the intensity function of a nonstationary Poisson process. The intensity function, Λ(t), − T < t < T, is a priori a second-order stochastic process. Estimators are found which minimize among, respectively, the class of step functions, the class of moving averages, and a class of linear estimators. An approximation for large T to the last estimator is found. These estimators are compared in a numerical example…

非平稳泊松过程强度函数的贝叶斯线性估计AI 解读

A Bayesian approach is taken to the problem of estimating the intensity function of a nonstationary Poisson process. The intensity function, Λ(t), − T < t < T, is a priori a second-order stochastic process. Estimators are found which minimize among, respectively, the class of step functions, the class of moving averages, and a class of linear estimators. An approximation for large T to the last estimator is found. These estimators are compared in a numerical example…

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独立泊松总体均值的同时估计AI 解读

A procedure is derived for simultaneously estimating the means of Poisson populations using independent samples. The total loss is the sum of component, standardized squared error losses. The derived procedure is minimax, generalized Bayes, admissible relative to a large class, and better than using the sample means as estimators of the corresponding population means. The latter procedure is compared with the derived procedure, both numerically and asymptotically.