| momentSK {gamlss.dist} | R Documentation |
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 |
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, ( |
exc.K0.01: |
excess centile kurtosis, ( |
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 |
The function centileKurt() for a given argument p produces:
p |
the value determiming the centile kurtosis |
Kp |
sample centile kurtosis at |
sKp |
sample standardised centile kurtosis at |
ex.Kp: |
sample excess centile kurtosis at |
teKp: |
sample transformed excess centile kurtosis at |
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, 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, 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. doi:10.1201/b21973
(see also https://www.gamlss.com/).
See Also
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")