momentSK: Sample and theoretical Moment and Centile Skewness and...

In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

Sample and theoretical Moment and Centile Skewness and Kurtosis Functions

Description

The functions momentSK(), centileSK(), centileSkew() and centileKurt(), calculate sample statistics related to skewness and kurtosis. The function theoCentileSK() calculates the theoretical centile statistics from a given gamlss.family distribution. The plotCentileSK() plots the theoretical centile skewness and kurtosis against p (see below).

The function checkMomentSK() can be use to check (a) whether the moment skewness and kurtosis of a fitted model are modelled adequantly (the residuals of the model are used). (b) whether a given sample display skewness or kurtosis.

Usage

momentSK(x,  weights=NULL)
centileSK(x, cent = c(1, 25), weights=NULL)
centileSkew(x, cent = 1, weights=NULL)
centileKurt(x, cent = 1, weights=NULL)

theoCentileSK(fam = "NO", p = 0.01, ...)
plotCentileSK(fam = "NO", plotting = c("skew", "kurt", "standKurt"), 
             add = FALSE, col = 1, lty = 1, lwd = 1, ylim = NULL, ...)
             
checkMomentSK(x, weights=NULL, add = FALSE, bootstrap = TRUE, no.bootstrap = 99, 
               col.bootstrap = "lightblue", pch.bootstrap = 21, 
               asCharacter = TRUE, col.point = "black", pch.point = 4, 
               lwd.point = 2,  text.to.show = NULL, cex.text = 1.5, 
               col.text = "black", show.legend = TRUE) 
               
checkCentileSK(x,weights=NULL, type = c("central", "tail"), add = FALSE, 
              bootstrap = TRUE, no.bootstrap = 99, 
              col.bootstrap = "lightblue", pch.bootstrap = 21, 
              asCharacter = TRUE, col.point = "black", pch.point = 4, 
              lwd.point = 2,  text.to.show = NULL, cex.text = 1.5, 
              col.text = "black", show.legend = TRUE)

Arguments

x	data vector or gamlss model
weights	prior weights for the x
cent	the centile required
type	For centile skewness and kurtosis only whether "central" (default) or "tail")
fam	A gamlss distribution family
plotting	what to plot
add	whether to add the line to the existing plot
col	the colour of the line
lty	the type of the line
lwd	the width of the line
ylim	the y limit of the graph
p	the value determiming the centile skewness or kurtosis
...	additional arguments pass to theoCentileSK() function i.e. the values of the distribution parameters
bootstrap	whether a plot of the bootstrap skewness and kurtosis measures should be added in the plot
no.bootstrap	the number of boostrap skewness and kurtosis measures
col.bootstrap	the coloue for boostraps
pch.bootstrap	the point type of boostraps
asCharacter	whether to plot the estimated skewness and kurtosis measure as character or as point
col.point	the colour of the skewness and kurtosis measure
pch.point	the point type of the skewness and kurtosis measure
lwd.point	the width of the plotted point
text.to.show	to display text different from variable or model
cex.text	the size of the text
col.text	the colour of the text
show.legend	whether to show the legent

Details

Those function calculate sample moment and centile skewness and kurtosis statistics and theoretical centile values for a specific distribution.

Value

Different functions produce different output: The function momentSK() produce:

mom.skew:	sample moment skewness
trans.mom.skew:	sample transformed moment skewness
mom.kurt:	sample moment kurtosis
excess.mom.kurt:	sample excess moment kurtosis
trans.mom.kurt:	sample ransformed moment excess kurtosis
jarque.bera.test:	the value of the Jarque-bera test for testing whether skewness and excess kurtosis are zero or not

The function centileSK() produces:

S0.25:	sample centile central skewness
S0.01:	sample centile tail skewness
K0.01:	sample centile kurtosis
standK0.01:	standardised centile kurtosis, (K0.01/3.449)
exc.K0.01:	excess centile kurtosis, (K0.01-3.449)
trans.K0.01:	transfored excess centile kurtosis, (exc.K0.01/(1+abs(exc.K0.01))

The function centileSkew() for a given argument p produces:

p:	the value determiming the centile skewness
Sp:	sample centile skewness at p

The function centileKurt() for a given argument p produces:

p	the value determiming the centile kurtosis
Kp	sample centile kurtosis at p
sKp	sample standardised centile kurtosis at p
ex.Kp:	sample excess centile kurtosis at p
teKp:	sample transformed excess centile kurtosis at p

The function theoCentileSK for a given gamlss.family produces:

IR	the interquartile range of the distribution
SIR	the semi interquartile range of the distribution
S_0.25	the central skewness of the distribution
S_0.01:	the tail skewness of the distribution
K_0.01:	the centile kurtosis of the distribution
sK_0.01:	the standardised centile kurtosis of the distribution

Author(s)

Mikis Stasinopoulos, Bobert Rigby, Gillain Heller and Fernanda De Bastiani.

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape, (with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/9780429298547")}. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v023.i07")}.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/b21973")}

(see also https://www.gamlss.com/).

See Also

gamlss.family

Examples

Y <- rSEP3(1000)
momentSK(Y)
centileSK(Y)
centileSkew(Y, cent=20)
centileKurt(Y, cent=30)

theoCentileSK("BCCG", mu=2, sigma=.2, nu=2)
plotCentileSK(fam="BCCG",  mu=2, sigma=.2, nu=2)

checkMomentSK(Y)
checkCentileSK(Y)
checkCentileSK(Y, type="tail")

gamlss.dist documentation built on Aug. 24, 2023, 1:06 a.m.