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随机变量乘积的分布AI 解读

Summary The problem of finding the probability density function of the product of n identically distributed independent normal variables was solved by Springer and Thompson (1966). Their formulae for n ≤ 7 are simplified in this paper and generalized to an arbitrary number of factors. Similar formulae for the corresponding probability distribution functions are derived. The applicability of these results to the cases of the negative exponential, Weibull and gamma…

统计谱分析中的带宽与分辨能力AI 解读

SUMMARY The purpose of this paper is to refute Grenander’s latest objections to the authors' work on statistical spectral analysis, and to clarify the distinction between resolvability, bandwidth, and bias.

随机过程谱密度函数的估计AI 解读

Summary On the basis of an expected-mean-square-error criterion, the authors discuss the various hitherto proposed estimators of the spectral density function of a discrete-parameter process; they also introduce a new estimator. Any of these estimators depends on some parameter, and indications are given as to how this parameter should match those of the process in order to optimize the estimator. The alleged conflict between resolvability and statistical reliability is…