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极值吸引域的检验AI 解读

A simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the Gumbel distribution. It is based on the top k order statistics and is a generalization of the Shapiro–Wilk goodness-of-fit statistic. The critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation. The power turns out to be…

泊松输入下近满水坝模型的进一步结果AI 解读

Summary The dam model investigated has infinite depth, unit release per unit time, and inputs which form a compound Poisson process. The time-dependent content distribution for arbitrary initial content is obtained explicitly by a direct method and its asymptotic properties are investigated. The distribution of the time to first overflow as well as the probability of no overflow are also obtained explicitly by a similar method.

具有泊松输入的近满水库模型AI 解读

Summary In this paper, the content of a dam with infinite depth, unit release per unit time and inputs which form a compound Poisson process is investigated by means of an integral equation technique. The Laplace transform of the content distribution for an initially full dam is calculated and inverted. The asymptotic behaviour of the content is described and its mean and variance obtained. Duality relationships with the almost empty dam with Poisson input are pointed out…