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叠加过程的组成过程数量估计AI 解读

We consider a superposition of an unknown number of independent homogeneous Poisson processes with unknown rates and suppose that when an event occurs, the component process in which it occurred can be identified. The number of component processes and their rates are to be estimated by observing the system for some time. In the general case, it is difficult to estimate all of the parameters but we derive the best unbiased estimators of some parametric functions. Inferences…

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利用再捕获抽样估计总体规模AI 解读

A design called recapture debugging is proposed to get extra information to estimate the original number of faults, N, in a reliability system. The system is observed for a fixed amount of time τ and the failures are assumed to follow an exponential law with an unknown common parameter λ. The maximum likelihood and moment estimators of N and λ are derived and compared with the existing estimators. The recapture sampling provides substantially more information and improved…

分组数据估计的基尼及相关不平等指数界限的大样本理论AI 解读

The joint asymptotic distribution of the upper and lower bounds for the Gini index derived by Gastwirth for grouped data are obtained. From them a conservative asymptotically distribution-free confidence interval for the population Gini index is presented. The methods also yield similar results for other indices of inequality (e.g., Theil's and Atkinson's).