创建具有特定时刻的分布曲线

Question

有没有办法在给定第 1 到第 4 个矩（均值、方差或标准差、偏度和峰度）的情况下创建分布曲线？这是一小部分 table 的描述性统计数据。第五个变量比其他变量有更强的正偏斜和更大的峰态，让我相信可能需要使用非正态分布。

dput(summarystats_factors)
structure(list(ERVALUEY = c(1.21178722715092, 8.4400515531338, 
0.226004674926861, 3.89328347004421), ERVOLY = c(0.590757887612924, 
7.48697754999463, 0.295973723450469, 3.31326615805655), ERQUALY = c(1.59367031426668, 
4.57371901763411, 0.601172123904339, 3.89080479205755), ERMOMTY = c(3.09719686678745, 
7.01446175391253, 0.260638252621096, 3.28326189430607), ERSIZEY = c(1.69935727981412, 
6.1917295410928, 1.24021163316834, 6.23493767854042), Moment = structure(c("Mean", 
"Standard Deviation", "Skewness", "Kurtosis"), .Dim = c(4L, 1L
))), row.names = c(NA, -4L), class = "data.frame")

Answer 1

使用 PearsonDS 包，pearson0 系列创建匹配指定时刻的“正态”分布，但其他选项可用。

Answer 2

我们可以使用 curve 和 PearsonDS::dpearson。请注意，moments= 参数需要 均值、方差、偏度、峰度 的顺序，因此数据的行必须相应地排序（就像你的情况一样）示例数据）。

FUN <- function(d, xlim, ylim, lab=colnames(d), main='Theoretical Distributions') {
  s <- seq(d)
  lapply(s, \(i) {
    curve(PearsonDS::dpearson(x, moments=d[, i]), col=i + 1, xlim=xlim, ylim=ylim, 
          add=ifelse(i == 1, FALSE, TRUE), ylab='y', main=main)
  })
  legend('topright', col=s + 1, lty=1, legend=lab, cex=.8, bty='n')
}

FUN(dat[-6], xlim=c(-2, 10), ylim=c(-.01, .2))

数据：

dat <- structure(list(ERVALUEY = c(1.21178722715092, 8.4400515531338, 
0.226004674926861, 3.89328347004421), ERVOLY = c(0.590757887612924, 
7.48697754999463, 0.295973723450469, 3.31326615805655), ERQUALY = c(1.59367031426668, 
4.57371901763411, 0.601172123904339, 3.89080479205755), ERMOMTY = c(3.09719686678745, 
7.01446175391253, 0.260638252621096, 3.28326189430607), ERSIZEY = c(1.69935727981412, 
6.1917295410928, 1.24021163316834, 6.23493767854042), Moment = structure(c("Mean", 
"Standard Deviation", "Skewness", "Kurtosis"), .Dim = c(4L, 1L
))), row.names = c(NA, -4L), class = "data.frame")

创建具有特定时刻的分布曲线

Creating distribution curves with specific moments

statistics

plot

r

distribution