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次序统计量矩的界与近似AI 解读

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given.

次序统计量矩的界与近似AI 解读

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given.

利用样本次序统计量逼近连续单变量总体的分位数函数AI 解读

Approximations to the mathematical relation between the variate value z and the unknown distribution function F of the continuous, univariate population from which a sample is available are obtained in which z is expressed as a series of polynomials in F; the coefficients are the expectations of linear combinations of the order statistics of the sample. A particular system of orthogonal polynomials and a particular system of n linearly independent linear systematic…

摘要暂缺

回归百分位点的判别区间AI 解读

In simple linear regression the 100pth percentile of the distribution of Y for a given value of X is β0 + β1 X + Zp σ, where Zp is the 100pth percentile of the standard normal distribution. The problem considered is to estimate the value of X for which this percentile is equal to some specified value, Yp . Both point and interval estimates are considered. A procedure for obtaining exact confidence intervals is derived, and in addition, two approximate and two conservative…

若干Rényi型统计量的有限样本临界值表AI 解读

Let X(1) ≤ X (2) ≤ … ≤ X (n) be an ordered sample of a random variable X which has continuous probability distribution function F (x), and let Fn (x) be the corresponding empirical distribution function. The following three statistics, introduced by A. Rényi, are considered: The paper presents table of exact probabilities for these statistics for finite sample sizes. The limiting distributions of these statistics for sample size n ∞ are discussed, and sample sizes are…

利用两个或三个次序统计量估计极值分布参数AI 解读

This paper discusses the use of order statistics in ostimating the parameters of the oxtreme value distribution. The best linear unbiased estimator of the location and scale parameter is given, based on two or three order statistics, for samples up to size 20. For very large samples, the analogous estimators based on sample quantiles are obtained.

关于概率与分位数的推断AI 解读

Summary It is intended to make inferences on the basis of a set of observations resulting from n replicates of an experiment, where each observation X has distribution F(x; θ), in order to provide information about a future performance of the same experiment, or a small number of such future performances. In such a situation the inference should concern the probability of an event occurring in the future experiment, rather than directly concern the parameter θ (a vector in…

摘要暂缺

摘要暂缺

Approximations to the mathematical relation between the variate value z and the unknown distribution function F of the continuous, univariate population from which a sample is available are obtained in which z is expressed as a series of polynomials in F; the coefficients are the expectations of linear combinations of the order statistics of the sample. A particular system of orthogonal polynomials and a particular system of n linearly independent linear systematic…

利用样本分位数估计逻辑斯蒂分布参数AI 解读

Large sample estimation of the mean and the standard deviation of the logistic distribution is discussed. Best linear unbiased estimates based on k = 2(1)9 sample quantiles are used. The optimum spacings, the coefficients to be used in computing the estimates and the variances and asymptotic efficiencies of the estimates are given. A comparison is obtained between the optimum spacings and spacing the observations using the expected values of order statistics.

利用两个或三个次序统计量估计极值分布参数AI 解读

This paper discusses the use of order statistics in ostimating the parameters of the oxtreme value distribution. The best linear unbiased estimator of the location and scale parameter is given, based on two or three order statistics, for samples up to size 20. For very large samples, the analogous estimators based on sample quantiles are obtained.

检验多个协方差矩阵相等AI 解读

A statistic which has been suggested for use in testing the equality of k covariance matrices is considered. Approximations to its distribution are briefly discussed and a table of significance points approximated from an asymptotic series expansion of the distribution function is given for certain parameter values.

逆高斯分布函数AI 解读

This note deals with a method of evaluating the distribution function of the Inverse Gaussian Distribution, from the Standard Normal Distribution.

样本分位数渐近分布的一则说明AI 解读

Summary This paper gives a rigorous proof, under conditions believed to be minimal, of the asymptotic normality of a finite set of quantiles of a random sample from an absolutely continuous distribution. The proof is substantially simpler than those that have previously been published.

双重非中心 t 分布的级数表示AI 解读

This paper gives analytic expressions for the distribution function of t″, a doubly noncentral t-distribution, with v degrees of freedom and noncentrality parameters δ and λ, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t″ ≤t| ν, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t = 0 and 1 are given in Table I.

用傅里叶级数估计概率密度与累积分布AI 解读

A class of estimators (referred to as the Fourier estimators m and m) of the probability density function f and the associated cumulative distribution function F are considered. Here m = Σmk=0 âkψk and m = Σmk=0 Âk ψk where the functions {ψk} comprise an orthogonal set with respect to weight function w(x), and the statistics âk and Âk are formed from the n unordered observations.Simple expressions are found for the mean integrated square errors, M.I.S.E., of the estimators m…

利用样本分位数分析超大样本极值数据AI 解读

This paper deals with estimating the location and the scale parameters of the extreme value distribution when the sample size is very large, using sample quantiles. An estimator is given for the location parameter when the scale parameter is known, based on one or more (up to 15) order statistics. Also given is an estimator for the scale parameter when the location parameter is known, built on two order statistics. An iterative procedure is utilized to estimate the…

若干互不相关的非参数检验统计量AI 解读

It is shown that odd translation invariant two sample statistics are uncorrelated with even translation invariant two sample statistics when the distribution function of the combined sample is equally symmetric. This is a generalization of a result of Hogg. It is used to establish conditions under which certain dispersion test statistics (including ones proposed by Lehmann, Mood, Ansari-Bradley-Freund-Barton-David, Klotz and Moses) are uncorrelated with certain location test…

用于因果分析与规划的新型收入不平等度量AI 解读

A new system of inequality indicators is introduced in the paper. It has been elaborated for measuring income inequalities, but can serve as inequality measures for other phenomena as well. The new indicators not only measure the degree of the inequality but are also suitable for measuring its economic motivation. Properties of the new measures, including large sample properties of their estimators, are discussed. The case of the lognormal distribution is of special…

以超几何级数表示的分布函数近似AI 解读

A general method of deriving asymptotic approximations to density and distribution functions is applied to various discrete distributions, particularly the hypergeometric, for which numerical comparisons with other approximations are given.

协方差矩阵检验统计量的分布AI 解读

A statistic is considered which has been proposed for testing whether a multivariate normal population covariance matrix is equal to a given matrix. Approximations to its distribution are derived, and comparisons are made by using a series expansion of the distribution function. A table of significance points obtained from the series is given for certain values of the parameters.

非平衡单因素随机分类中随机效应与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…