这种分布的获得方法如下。让x是一个围绕原点对称连续的，大小为n的分布的样本。那Wilcoxon签名秩统计是x[i]为正的绝对值x[i]的秩之和。这个统计量的取值在0和n(n+1)/2之间，其平均值和方差分别为n(n+1)/4和n(n+1)(2n+1)/24。如果前两个参数中的任何一个是一个向量，则使用循环规则对两者的所有组合进行计算，直至较长的向量的长度。
Distribution of the Wilcoxon Signed Rank Statistic DescriptionDensity, distribution function, quantile function and random generation for the distribution of the Wilcoxon Signed Rank statistic obtained from a sample with size n.
Usagedsignrank(x, n, log = FALSE) psignrank(q, n, lower.tail = TRUE, log.p = FALSE) qsignrank(p, n, lower.tail = TRUE, log.p = FALSE) rsignrank(nn, n)Arguments
| x, q | vector of quantiles. |
| p | vector of probabilities. |
| nn | number of observations. If length(nn) > 1, the length is taken to be the number required. |
| n | number(s) of observations in the sample(s). A positive integer, or a vector of such integers. |
| log, log.p | logical; if TRUE, probabilities p are given as log(p). |
| lower.tail | logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
#### 威尔科克森符号秩和(Wilcoxon Signed Rank statistic)分布 # 1.威尔科克森符号秩和分布中抽样函数rsignrank nn <- 100 rsignrank(nn, n=10) # 2.威尔科克森符号秩和分布概率密度函数 x <- 1:100 y <- dsignrank(x, 20) plot(x,y) # 3.威尔科克森符号秩和分布累积概率 # P[X ≤ x] psignrank(30,n = 10) # P[X > x] psignrank(30,n = 10,lower.tail = FALSE) # probabilities p are given as log(p). psignrank(2,n = 5,log.p = TRUE) # 4.分位数函数qsignrank(psignrank的反函数) # 累积概率为0.95时的x值 # x <- seq(1,100) # plot(x,psignrank(x, n = 10)) qsignrank(0.95,n = 10) qsignrank(0.995,n = 10)
