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基于熵的均匀性检验AI 解读

The power properties of an entropy-based test are investigated when used for testing uniformity on [0, 1]. Percentage points and power against seven alternatives are reported. Compared with other tests of uniformity, the entropy-based test possesses good power properties for many alternatives. Some asymptotic null and alternative distributions are derived. For sample sizes up to 100 the table of percentage points provides a practical guide for using this test. A theory of…

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排序总体均值的双侧置信区间AI 解读

Suppose given k(≥2) populations π1, ···, πk such that observations from population πi have density function f(x—θi), x∈R, where the location parameter θi is unknown (1 ≤ i ≤ k). Assume Ef ≡ ∫∞ -∞ xf(x)dx < ∞. Let the population means be denoted by μ1, ···, μk and their ranked values by μ[1] ≤ ··· ≤ μ[k]. Dudewicz [1] gave upper and lower confidence intervals for μ[i](1 ≤ i ≤ k). We use these to obtain a class of two-sided intervals. For μ[k] Lal Saxena and Tong [2]…

非参数选择程序的效率：最大位置参数情形AI 解读

Suppose that X1, ···, Xk are mutually independent observations from populations π1, ···, πk and that Xi has a density fxi(·)(1 ≤ i ≤ k). For i = 1, ···, k let pi = P[Xi > maxj ≠ i Xj], and let p[k] = max (p1, ···, pk). Bechhofer and Sobel [4] have proposed a nonparametric selection procedure based on multinomial random variables for the problem of selecting a population which has the highest probability, p[k], of producing the largest observation. (The density fxi(·) may be…