A bucket plot is a graphical way to check the skewness and kurtosis of a continuous variable or the residuals of a fitted GAMLSS model. It plots the transformed moment skewness and transformed moment kurtosis of the variable (or residuals) together with a cloud of points obtained using a non-parametric bootstrap from the original variable (or residuals). It also provides a graphical way of performing the Jarque-Bera test (JarqueandBera,1980).

There are two different bucket plots specified by the `type`

argument:

i) the `moment`

bucket and
ii) the `centile`

bucket which itself can be `central`

or `tail`

one.

```
bp(obj = NULL, weights = NULL,
type = c("moment", "centile.central", "centile.tail"),
xvar = NULL, bootstrap = TRUE, no.bootstrap = 99,
col.bootstrap = c("lightblue", "pink", "khaki",
"thistle", "tan", "sienna1","steelblue", "coral", "gold",
"cyan"),
pch.bootstrap = rep(21, 10), asCharacter = TRUE,
col.point = rep("black", 10), pch.point = 1:10,
lwd.point = 2, text.to.show = NULL, cex.text = 1.5,
col.text = "black", show.legend = FALSE, n.inter = 4,
xcut.points = NULL, overlap = 0, show.given = TRUE,
cex = 1, pch = 21, data = NULL,
bar.bg = c(num = "lightblue", fac = "pink"), ...)
```

A plot displaying the transformed moment skewness and transformed moment kurtosis of the sample or residual of a model.

- obj
A

`gamlss`

fitted object.- weights
prior weights.

- type
type of bucket plot whether "moment", "centile.central", or "centile.tail".

- xvar
the x-variable if need to split the bucket plot.

- bootstrap
whether to bootstrap the skewness and kurtosis points

- no.bootstrap
the number of the bootstrap samples in the plot

- col.bootstrap
the colour of the bootstrap samples in the plot

- pch.bootstrap
the character plotting symbol.

- asCharacter
whether to plot the skewness and kurtosis as character or just points.

- col.point
the colout of the point is plotted as point

- pch.point
the character symbol for the point

- lwd.point
the width of the symbol

- text.to.show
whether to show character for the model

- cex.text
the

`cex`

of the text- col.text
the

`colour`

of the text- show.legend
whether to show the legend

- n.inter
number of intervals

- xcut.points
cut points for the

`xvar`

if need- overlap
whether the interval id

`xvar`

is set should overlap- show.given
showing the top part of the plot

- cex
the

`cex`

- pch
the point character

`pch`

- data
if data has to be set

- bar.bg
the backgroud color of the bars in the top of the figure

- ...
other arguments

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk and Fernanda De Bastiani

De Bastiani, F., Stasinopoulos, D. M., Rigby, R. A., Heller, G. Z., and Lucas A. (2022) Bucket Plot: A Visual Tool for Skewness and Kurtosis Comparisons. send for publication.

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. 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, 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. tools:::Rd_expr_doi("10.1201/b21973")

Stasinopoulos, M. D., Rigby, R. A., and De Bastiani F., (2018) GAMLSS: a distributional regression approach, *Statistical Modelling*, Vol. **18**,
pp, 248-273, SAGE Publications Sage India: New Delhi, India. tools:::Rd_expr_doi("10.1177/1471082X18759144")

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

`wp, Q.stats`

```
m1 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA)
bp(m1)
```

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