This function provides four plots for checking the normalized (randomized for a discrete response distribution) quantile
residuals of a fitted GAMLSS object, referred to as residuals below : a plot of residuals against fitted values, a plot of the residuals against
an index or a specific explanatory variable, a density plot of the residuals and a normal Q-Q plot of the residuals.
If argument `ts=TRUE`

then the first two plots are replaced by the autocorrelation function (ACF) and partial autocorrelation function (PACF)
of the residuals

```
# S3 method for gamlss
plot(x, xvar = NULL, parameters = NULL, ts = FALSE,
summaries = TRUE, ...)
```

Returns four plots related to the residuals of the fitted GAMLSS model and prints summary statistics for the residuals if the `summary=T`

- x
a GAMLSS fitted object

- xvar
an explanatory variable to plot the residuals against

- parameters
plotting parameters can be specified here

- ts
set this to TRUE if ACF and PACF plots of the residuals are required

- summaries
set this to FALSE if no summary statistics of the residuals are required

- ...
further arguments passed to or from other methods.

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby and Kalliope Akantziliotou

This function provides four plots for checking the normalized (randomized) quantile residuals (called `residuals`

) of a fitted GAMLSS object.
Randomization is only performed for discrete response variables. The four plots are

residuals against the fitted values (or ACF of the residuals if

`ts=TRUE`

)residuals against an index or specified x-variable (or PACF of the residuals if

`ts=TRUE`

)kernel density estimate of the residuals

QQ-normal plot of the residuals

For time series response variables option `ts=TRUE`

can be used to plot the ACF and PACF functions of the residuals.

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. 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, https://www.jstatsoft.org/v23/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.

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

`gamlss`

```
data(aids)
a<-gamlss(y~pb(x)+qrt,family=PO,data=aids)
plot(a)
rm(a)
```

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