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选定次序统计量的伴随变量最大值的分布AI 解读

For a random sample of size $n$ from an absolutely continuous bivariate population $(X, Y)$, let $X_{i:n}$ denote the $i$th order statistic of the $X$ sample values. The $Y$-value associated with $X_{i:n}$ is denoted by $Y_{\lbrack i:n\rbrack}$ and is called the concomitant of the $i$th order statistic. For $1 \leq k \leq n$, let $V_{k,n} = \max(Y_{\lbrack n - k + 1: n\rbrack},\ldots,Y_{\lbrack n: n\rbrack})$. In this paper, we discuss the finite-sample and the asymptotic…

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对称分布中异常值对位置 L 估计量的影响AI 解读

The effect is studied of an outlier which has the same symmetric distribution as the other observations except for a change in location and a possible increase in scale. We show that the median is the most bias-resistant estimator, in the class of L-statistics with symmetric nonnegative coefficients that add up to one, for a class of distributions which includes the normal, double-exponential and logistic distributions.

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分布局部变异的度量：间距期望与次序统计量方差AI 解读

Two measures of variation about the rth order statistic Xr:n are studied: the expected value of the spacing Xr+1:n −Xr:n and the variance of Xr:n. The nature of the dependence of these measures on r, for n fixed, is examined for various classes of distributions. In the case of the variance of Xr:n the situations considered are supplemented by some asymptotic results.

次序统计量伴随变量之秩的分布与期望AI 解读

Let $(X_i, Y_i)$ be $n$ independent rv's having a common bivariate distribution. When the $X_i$ are arranged in nondecreasing order as the order statistics $X_{r:n} (r = 1,2,\cdots, n)$, the $Y$-variate $Y_{\lbrack r:n\rbrack}$ paired with $X_{r:n}$ is termed the concomitant of the $r$th order statistic. The small-sample theory of the distribution and expected value of the rank $R_{r:n}$ of $Y_{\lbrack r:n\rbrack}$ is studied. In the special case of bivariate normality an…

等待时间悖论与次序统计量AI 解读

It is well known that we tend to have to wait longer than we expect. Special cases of this paradox have been discussed by Feller and by Zelen. Here the paradox is further explored, and generalizations are considered to describe the effect of the observer on the expected length of an interval between successive events in a life test.

等待时间悖论与次序统计量AI 解读

It is well known that we tend to have to wait longer than we expect. Special cases of this paradox have been discussed by Feller and by Zelen. Here the paradox is further explored, and generalizations are considered to describe the effect of the observer on the expected length of an interval between successive events in a life test.

离散总体与分组样本的次序统计量AI 解读

The aim of this paper is two-fold: (1) To give a unified treatment of the theory of order statistics when the parent distribution is not necessarily continuous. (2) To assess the effects of grouping on the distribution of order statistics and to indicate the convenience, under suitable conditions, of using order statistics for the estimation of parameters from grouped data with or without censoring.

独立同分布离散随机变量之和的精确分布AI 解读

Let Sn be the sum of n independent discrete variates with common probability distribution px (x = 0, 1, 2, [mdot][mdot][mdot]). A table is presented which allows Pr (Sn = s) to be written down, for any n and for s ≤15, as a finite series involving mixed powers of the px 's. If the range of x is finite (x ≤ m) the table will also give Pr(Sn = mn - s). The use of the table is illustrated and several applications are indicated.

独立同分布离散随机变量之和的精确分布AI 解读

Let Sn be the sum of n independent discrete variates with common probability distribution px (x = 0, 1, 2, [mdot][mdot][mdot]). A table is presented which allows Pr (Sn = s) to be written down, for any n and for s ≤15, as a finite series involving mixed powers of the px 's. If the range of x is finite (x ≤ m) the table will also give Pr(Sn = mn - s). The use of the table is illustrated and several applications are indicated.

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负阶矩与比率统计量AI 解读

Summary A simple method is considered of obtaining the moments of the sampling distribution of a ratio, when the numerator and denominator are independent.

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单个正态样本中极差与标准差之比的分布AI 解读

H. A. DAVID, H. O. HARTLEY, E. S. PEARSON; THE DISTRIBUTION OF THE RATIO, IN A SINGLE NORMAL SAMPLE, OF RANGE TO STANDARD DEVIATION, Biometrika, Volume 41,