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正态混合与正态 A 型分布抽样分布的讨论（统计量缺失）AI 解读

The asymptotic method described in an earlier article (Bowman and Shenton [2]) is applied to derive the power of the test of normality against skewed alternatives. In particular, normal mixtures of two components and Type A distributions, each depending on four parameters, are considered. Comparisons of the assessment of percentage points of using Cornish-Fisher expansions based on the normal and Monte Carlo simulations are given.

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双成分正态混合模型的解空间AI 解读

The space of acceptable solutions for the sum of two normal components involving five parameters, with means and variances different, is described in terms of the three standard cumulants, k3, k4 and k5. It is assumed that the mixture is being fitted by moments to a given theoretical distribution. A number of sections for k5 constant are given.

序列相关系数的矩AI 解读

Summary For a discrete first-order auto-regressive scheme (with initial value zero) xt = αxt-1 + ϵt, expressions have been found for the first four moments of α̂=∑1nxtxt−1/∑1n−1xt2. The expressions are of two kinds : (i) series in ascending powers of α2, (ii) asymptotic series in descending powers of n. A table of values of μ1‱,σ(α̂),β1(α̂),β2(α̂) is included. For the special case α2 = 1 the dominant terms in the first four moments are stated.

最大似然估计量的高阶矩AI 解读

SUMMARY For a distribution depending on a single parameter the first four sampling moments of the maximum-likelihood estimate to orders N−2, N−3, N−3 and N−4 respectively are given. Expressions for the measures of skewness γ1 and γ2 are also given. Several illustrative examples are included as a check on the heavy algebra. The paper extends earlier work by Haldane and Smith.

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固定巡检间隔下自动络筒机的效率AI 解读

Summary The problem is that of maximizing the average efficiency of a machine which (i) stops when its total running time has reached a fixed value a, (ii) has accidental stops, and (iii) is patrolled for servicing (i.e. re-starting if necessary) at a fixed interval p which may be less than a, efficiency being defined as the ratio of the running time to the total time under consideration. The probability distribution of the number of patrols required to exhaust the total…

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Summary The main results in both the discrete and continuous cases are summarized side by side in Tables 8 a and 8 b .

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