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四字母词：环形排列中模式频数的分布AI 解读

Summary An alphabet of c letters is considered. There are, then, ck possible ordered sequences of k of these. Such k-sequences are grouped into λ mutually exclusive and exhaustive sets; members of each set (called k-patterns) are counted the same. A general expression for the joint generating function of the frequencies of occurrence of the different k-patterns is obtained when r letters, with fixed numbers of each sort, are randomly arranged in a ring. In particular,…

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Generating Functions Recurrent Events Random Walk Models Markov Chains Discrete Branching Processes Markov Processes in Continuous Time Homogeneous Birth and Death Processes Some Non-Homogeneous Processes Multi-Dimensional Processes Queueing Processes Epidemic Processes Competition and Predation Diffusion Processes Approximations to Stochastic Processes Some Non-Markovian Processes.

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简单依赖下多事件链的持续性AI 解读

D. E. BARTON, F. N. DAVID, EVELYN FIX; Persistence in a chain of multiple events when there is simple dependence, Biometrika, Volume 49, Issue 3-4, 1 Janua

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非中心 F 分布对数的若干性质AI 解读

E2= fiF* f2 +f1 F* it was studied by Wishart (1932) and by Tang (1938) who gave a few values of the probability integral. Patnaik (1949) approximated to the distribution of F* by a central F distribution. It is clear that any tabulation of the distribution of F* will be a formidable proceeding. There are three parameters fl, f2 and A which intervene explicitly. If we are concemed with the power function of the F-test there must also be the values of the central F at which…

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匹配分布：Poisson 极限形式与近似方法AI 解读

SUMMARY (1) The Matching Problem is reviewed. (2) Stevens’s approach is generalized to yield the explicit results so far known. (3) A continuous range of Poisson limits is derived for the various matching distributions by an elementary method (alternative to Kaplansky’s symbolic proof). (4) The approximations afforded by some of these are improved by orthogonal polynomial fitting. (5) Further Poisson limits are derived for certain general classes of multiple matching…

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适用于截断数据的两类位置变化检验比较AI 解读

Summary The powers of one and two-sample tests of change of centre of location based on the difference of sample quantiles are compared with those of the corresponding combinatorial tests based on quantile division of the sample. The powers are found to be asymptotically equivalent. Computation of particular cases suggests that for quite small samples there is good agreement of the powers of the two kinds of test with each other and with their common limiting form.

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按长度排序的随机区间若干注记AI 解读

Summary The joint probability distribution of several magnitudinally ordered intervals of a line is derived together with a moment generating function belonging to it. Some limiting distributions are given and the rate of convergence is examined. The distributions of some simple functions such as the ratio and difference of two ordered intervals are derived.

一类使最大似然估计在所有样本量下均无偏且方差最小的分布AI 解读

D. E. BARTON; A class of distributions for which the maximum-likelihood estimator is unbiased and of minimum variance for all sample sizes, Biometrika, Volume 4

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