r - 偏度和峰度的置信区间和标准误差

Question

请告诉我如何计算偏度和峰度以及它们各自的标准误差和与之相关的置信区间(即偏度的 SE 和峰度的 S.E)我找到了两个包

1) package:'measure'只能计算偏度和峰度

2) package:'rela' 可以同时计算偏度和峰度，但默认使用 bootstrap，并且在计算过程中没有命令将其关闭。

Answer 1

我只是复制并粘贴了 Howard Seltman 在 here 中发布的代码:

# Skewness and kurtosis and their standard errors as implement by SPSS
#
# Reference: pp 451-452 of
# http://support.spss.com/ProductsExt/SPSS/Documentation/Manuals/16.0/SPSS 16.0 Algorithms.pdf
# 
# See also: Suggestion for Using Powerful and Informative Tests of Normality,
# Ralph B. D'Agostino, Albert Belanger, Ralph B. D'Agostino, Jr.,
# The American Statistician, Vol. 44, No. 4 (Nov., 1990), pp. 316-321

spssSkewKurtosis=function(x) {
  w=length(x)
  m1=mean(x)
  m2=sum((x-m1)^2)
  m3=sum((x-m1)^3)
  m4=sum((x-m1)^4)
  s1=sd(x)
  skew=w*m3/(w-1)/(w-2)/s1^3
  sdskew=sqrt( 6*w*(w-1) / ((w-2)*(w+1)*(w+3)) )
  kurtosis=(w*(w+1)*m4 - 3*m2^2*(w-1)) / ((w-1)*(w-2)*(w-3)*s1^4)
  sdkurtosis=sqrt( 4*(w^2-1) * sdskew^2 / ((w-3)*(w+5)) )
  mat=matrix(c(skew,kurtosis, sdskew,sdkurtosis), 2,
        dimnames=list(c("skew","kurtosis"), c("estimate","se")))
  return(mat)
}

要获得变量的偏度和峰度及其标准误差，只需运行此函数:

x <- rnorm(100)
spssSkewKurtosis(x)

##             estimate    se
##    skew       -0.684 0.241
##    kurtosis    0.273 0.478