Variance, robust spread measures, skewness and kurtosis

TODO

• link to diagDistributions, varianceHom

Install required packages

DescTools, robustbase

wants <- c("DescTools", "robustbase")
has   <- wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])

Variance and standard deviation

Corrected (sample) variance and standard deviation

age <- c(17, 30, 30, 25, 23, 21)
N   <- length(age)
M   <- mean(age)
var(age)

[1] 26.26667

sd(age)

[1] 5.125102

Uncorrected (population) variance and standard deviation

(cML <- cov.wt(as.matrix(age), method="ML"))

$cov
         [,1]
[1,] 21.88889

$center
[1] 24.33333

$n.obs
[1] 6

(vML <- diag(cML$cov))

[1] 21.88889

sqrt(vML)

[1] 4.678556

Robust spread measures

Winsorized variance and standard deviation

library(DescTools)
border  <- quantile(age, probs=c(0.2, 0.8))
ageWins <- Winsorize(age, val=border)
var(ageWins)

[1] 17.2

sd(ageWins)

[1] 4.147288

Inter-quartile-range

quantile(age)

   0%   25%   50%   75%  100% 
17.00 21.50 24.00 28.75 30.00 

IQR(age)

[1] 7.25

Mean absolute difference to the median

library(DescTools)
MeanAD(age)

[1] 4

Median absolute difference to the median (MAD)

mad(age)

[1] 6.6717

\(Q_{n}\): more efficient alternative to MAD

library(robustbase)
Qn(age)

[1] 6.792788

\(\tau\) estimate of scale

scaleTau2(age)

[1] 4.865323

Diversity of categorical data

fac <- factor(c("C", "D", "A", "D", "E", "D", "C", "E", "E", "B", "E"),
              levels=c(LETTERS[1:5], "Q"))
P   <- nlevels(fac)
(Fj <- prop.table(table(fac)))

fac
         A          B          C          D          E          Q 
0.09090909 0.09090909 0.18181818 0.27272727 0.36363636 0.00000000 

First, calculate Shannon index, then diversity measure.

library(DescTools)
shannonIdx <- Entropy(Fj, base=exp(1))
(H <- (1/log(P)) * shannonIdx)

[1] 0.8193845

Higher moments: skewness and kurtosis

library(DescTools)
Skew(age, method=2)

[1] -0.155005

Kurt(age, method=2)

[1] -1.094785

Detach (automatically) loaded packages (if possible)

try(detach(package:robustbase))
try(detach(package:DescTools))

Get the article source from GitHub

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