| Type: | Package |
| Title: | Generating and Fitting Truncated ‘gamlss.family’ Distributions |
| Version: | 5.1-9 |
| Date: | 2024-01-28 |
| Author: | Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>, Bob Rigby <r.rigby@gre.ac.uk> |
| Maintainer: | Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk> |
| LazyLoad: | yes |
| Depends: | R (≥ 2.2.1), gamlss.dist, gamlss (≥ 5.0-0), methods |
| Description: | This is an add on package to GAMLSS. The purpose of this package is to allow users to defined truncated distributions in GAMLSS models. The main function gen.trun() generates truncated version of an existing GAMLSS family distribution. |
| License: | GPL-2 | GPL-3 |
| URL: | https://www.gamlss.com/ |
| NeedsCompilation: | no |
| Packaged: | 2024-01-28 10:03:10 UTC; dimitriosstasinopoulos |
| Repository: | CRAN |
| Date/Publication: | 2024-01-30 08:00:03 UTC |
Generating and Fitting Truncated ‘gamlss.family’ Distributions
Description
This is an add on package to GAMLSS. The purpose of this package is to allow users to defined truncated distributions in GAMLSS models. The main function gen.trun() generates truncated version of an existing GAMLSS family distribution.
Details
The DESCRIPTION file:
| Package: | gamlss.tr |
| Type: | Package |
| Title: | Generating and Fitting Truncated `gamlss.family' Distributions |
| Version: | 5.1-9 |
| Date: | 2024-01-28 |
| Author: | Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>, Bob Rigby <r.rigby@gre.ac.uk> |
| Maintainer: | Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk> |
| LazyLoad: | yes |
| Depends: | R (>= 2.2.1), gamlss.dist, gamlss (>= 5.0-0), methods |
| Description: | This is an add on package to GAMLSS. The purpose of this package is to allow users to defined truncated distributions in GAMLSS models. The main function gen.trun() generates truncated version of an existing GAMLSS family distribution. |
| License: | GPL-2 | GPL-3 |
| URL: | https://www.gamlss.com/ |
Index of help topics:
fitTail For fitting truncated distribution to the tails
of data
gamlss.tr-package Generating and Fitting Truncated
'gamlss.family' Distributions
gen.trun Generates a truncated distribution from a
gamlss.family
trun Fits a Truncate Distribution from a
gamlss.family
trun.d Truncated Probability Density Function of a
gamlss.family Distribution
trun.p Truncated Cumulative Density Function of a
gamlss.family Distribution
trun.q Truncated Inverse Cumulative Density Function
of a gamlss.family Distribution
trun.r Generates Random Values from a Truncated
Density Function of a gamlss.family
Distribution
Author(s)
Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>, Bob Rigby <r.rigby@gre.ac.uk>
Maintainer: Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>
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. 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/).
Examples
# generating a t-distribution from 0 to 100
gen.trun(par=c(0,100),family="TF", name="0to100", type="both")
op<-par(mfrow=c(2,2))
plot(function(x) dTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="pdf")
plot(function(x) pTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="cdf")
plot(function(x) qTF0to100(x, mu=80 ,sigma=20, nu=5), 0.01, .999, ylab="invcdf")
hist(s1<-rTF0to100(1000, mu=80 ,sigma=20, nu=5), ylab="hist", xlab="x", main="generated data")
par(op)
For fitting truncated distribution to the tails of data
Description
There are two functions here. The function fitTail() which fits a truncated distribution to certain percentage of the tail of a response variable and the function fitTailAll() which does a sequence of truncated fits. Plotting the results from those fits is analogous to the Hill plot, Hill (1975).
Usage
fitTail(y, family = "WEI3", percentage = 10, howmany = NULL,
type = c("right", "left"), ...)
fitTailAll(y, family = "WEI3", percentage = 10, howmany = NULL,
type = c("right", "left"), plot = TRUE,
print = TRUE, save = FALSE, start = 5, trace = 0, ...)
Arguments
y |
The variable of interest |
family |
a |
percentage |
what percentage of the tail need to be modelled, default is 10% |
howmany |
how many observations in the tail needed. This is an alternative to |
type |
which tall needs checking the right (default) of the left |
plot |
whether to plot with default equal |
print |
whether to print the coefficients with default equal |
save |
whether to save the fitted linear model with default equal |
start |
where to start fitting from the tail of the data |
trace |
0: no output 1: minimal 2: print estimates |
... |
for further argument to the fitting function |
Details
The idea here is to fit a truncated distribution to the tail of the data. Truncated log-normal and Weibull distributions could be appropriate distributions. More details can be found in Chapter 6 of "The Distribution Toolbox of GAMLSS" book which can be found in https://www.gamlss.com/).
Value
A fitted gamlss model
Author(s)
Bob Rigby r.rigby@gre.ac.uk, Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Vlassios Voudouris
References
Hill B. M. (1975) A Simple General Approach to Inference About the Tail of a Distribution Ann. Statist. Volume 3, Number 5, pp 1163-1174.
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/).
See Also
Examples
data(film90)
F90 <- exp(film90$lborev1)# original scale
# trucated plots
# 10%
w403<- fitTail(F90, family=WEI3)
qqnorm(resid(w403))
abline(0,1, col="red")
## Not run:
# hill -sequential plot 10
w1<-fitTailAll(F90)
# plot sigma
plot(w1[,2])
#-----------------
#LOGNO
l403<- fitTail(F90, family=LOGNO)
plot(l403)
qqnorm(resid(l403))
abline(0,1)
# hill -sequential plot 10
l1<-fitTailAll(F90, family=LOGNO)
plot(l1[,2])
#-------------------------
## End(Not run)
Generates a truncated distribution from a gamlss.family
Description
The gen.trun() function allows the user to generate d, p, q, and r distribution functions plus an extra
gamlss.family function for fitting a truncated distribution with gamlss.
For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).
If the user want a different link (rather the default) for any of the parameters she/he has to declare at the generation of the functions, see example.
Usage
gen.trun(par = c(0), family = "NO", name = "tr",
type = c("left", "right", "both"),
varying = FALSE, print=TRUE, ...)
Arguments
par |
a vector with one (for |
family |
a |
name |
the extra characters to be added to the name of new truncated distribution, by default it adds |
type |
whether |
varying |
whether the truncation varies for different observations. This can be useful in regression analysis. If |
print |
whether to print the names of the created distribution |
... |
for extra arguments |
Value
Returns the d, the p, the q, the r and the fitting functions of a truncated gamlss.family distribution.
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/).
See Also
trun.d, trun.p, trun.q, trun.r
Examples
# generating a t-distribution from 0 to 100
gen.trun(par=c(0,100),family="TF", name="0to100", type="both")
op<-par(mfrow=c(2,2))
plot(function(x) dTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="pdf")
plot(function(x) pTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="cdf")
plot(function(x) qTF0to100(x, mu=80 ,sigma=20, nu=5), 0.01, .999, ylab="invcdf")
hist(s1<-rTF0to100(1000, mu=80 ,sigma=20, nu=5), ylab="hist", xlab="x",
main="generated data")
par(op)
m1<-histDist(s1, family=TF0to100, xlim=c(0,100))# fitting the data
# using the argumnt varying
# left part varies right part equal 100
leftPAR <- rPO(100)
gen.trun(par=cbind(leftPAR,rep(100, 100)),family="TF", name="0to100Varying",
type="both", varying=TRUE)
YY<- rTF0to100Varying(100, mu=80, sigma=20, nu=5)
m1<-gamlss(YY~1, family=TF0to100Varying)
m1
Fits a Truncate Distribution from a gamlss.family
Description
This function can be used to fit truncated distributions. It takes as an argument an existing GAMLSS family distribution and
a parameter vector, of the type c(left.value, right.value), and generates a gamlss.family object which then can be used to fit
a truncated distribution.
Usage
trun(par = c(0), family = "NO", type = c("left", "right", "both"), name = "tr",
local = TRUE, delta=NULL, varying = FALSE, ...)
Arguments
par |
a vector with one (for |
family |
an existing |
type |
what type of truncation is required, |
name |
a character string to be added to name of the created object i.e. with |
local |
if TRUE the function will try to find the environment of |
delta |
the delta increment used in the numerical derivatives |
varying |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |
... |
for extra arguments |
Details
This function is created to help the user to fit a truncated form of existing gamlss distribution.
It does this by taking an existing gamlss.family and changing some of the components of the distribution to help the fitting process.
It particular it i) creates a pdf (d) and a cdf (p) function within gamlss,
ii) changes the global deviance function G.dev.incr, the first derivative functions (see note below) and the quantile residual function.
Value
It returns a gamlss.family object which has all the components needed for fitting a distribution in gamlss.
Note
This function is experimental and could be changed. The function trun changes
the first derivatives of the original gamlss family d function to numerical derivatives
for the new truncated d function. The default increment delta,
for this numerical derivatives function, is eps * pmax(abs(x), 1) where
eps<-sqrt(.Machine$double.eps). The default delta could be inappropriate
for specific applications and can be overwritten by using the argument delta.
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/).
See Also
trun.d, trun.p, trun.q, trun.r, gen.trun
Examples
# generate a left truncated zero t family
gen.trun(0,family="TF")
# take a random sample of 1000 observations
sam<-rTFtr(1000,mu=10,sigma=5, nu=5 )
hist(sam)
# fit the distribution to the data
mod1<-gamlss(sam~1, family=trun(0,TF))
mod1
# now create a gamlss.family object before the fitting
Ttruc.Zero<- trun(par=0,family=TF, local=FALSE)
mod2<-gamlss(sam~1, family=Ttruc.Zero)
# now check the sensitivity of delta
Ttruc.Zero<- trun(par=0,family=TF, local=FALSE, delta=c(0.01,0.01, 0.01))
mod3<-gamlss(sam~1, family=Ttruc.Zero)
Truncated Probability Density Function of a gamlss.family Distribution
Description
Creates a truncated probability density function version from a current GAMLSS family distribution
For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).
Usage
trun.d(par, family = "NO", type = c("left", "right", "both"),
varying = FALSE, ...)
Arguments
par |
a vector with one (for |
family |
a |
type |
whether |
varying |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |
... |
for extra arguments |
Value
Returns a d family function
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/).
See Also
trun.p, trun.q, trun.r, gen.trun
Examples
#------------------------------------------------------------------------------------------
# continuous distribution
# left truncation
test1<-trun.d(par=c(0), family="TF", type="left")
test1(1)
dTF(1)/(1-pTF(0))
if(abs(test1(1)-(dTF(1)/pTF(0)))>0.00001) stop("error in left trucation")
test1(1, log=TRUE)
log(dTF(1)/(1-pTF(0)))
if(abs(test1(1, log=TRUE)-log(dTF(1)/pTF(0)))>0.00001)
stop("error in left trucation")
integrate(function(x) test1(x, mu=-2, sigma=1, nu=1),0,Inf)
# the pdf is defined even with negative mu
integrate(function(x) test1(x, mu=0, sigma=10, nu=1),0,Inf)
integrate(function(x) test1(x, mu=5, sigma=5, nu=10),0,Inf)
plot(function(x) test1(x, mu=-3, sigma=1, nu=1),0,10)
plot(function(x) test1(x, mu=3, sigma=5, nu=10),0,10)
#----------------------------------------------------------------------------------------
# right truncation
test2<-trun.d(par=c(10), family="BCT", type="right")
test2(1)
dBCT(1)/(pBCT(10))
#if(abs(test2(1)-(dBCT(1)/pBCT(10)))>0.00001) stop("error in right trucation")
test2(1, log=TRUE)
log(dBCT(1)/(pBCT(10)))
if(abs(test2(1, log=TRUE)-log(dBCT(1)/(pBCT(10))))>0.00001)
stop("error in right trucation")
integrate(function(x) test2(x, mu=2, sigma=1, nu=1),0,10)
integrate(function(x) test2(x, mu=2, sigma=.1, nu=1),0,10)
integrate(function(x) test2(x, mu=2, sigma=.1, nu=10),0,10)
plot(function(x) test2(x, mu=2, sigma=.1, nu=1),0,10)
plot(function(x) test2(x, mu=2, sigma=1, nu=1),0,10)
#-----------------------------------------------------------------------------------------
# both left and right truncation
test3<-trun.d(par=c(-3,3), family="TF", type="both")
test3(0)
dTF(0)/(pTF(3)-pTF(-3))
if(abs(test3(0)-dTF(0)/(pTF(3)-pTF(-3)))>0.00001)
stop("error in right trucation")
test3(0, log=TRUE)
log(dTF(0)/(pTF(3)-pTF(-3)))
if(abs(test3(0, log=TRUE)-log(dTF(0)/(pTF(3)-pTF(-3))))>0.00001)
stop("error in both trucation")
plot(function(x) test3(x, mu=0, sigma=1, nu=1),-3,3)
integrate(function(x) test3(x, mu=2, sigma=1, nu=1),-3,3)
#-----------------------------------------------------------------------------------------
# discrete distribution
# left
# Poisson truncated at zero means zero is excluded
test4<-trun.d(par=c(0), family="PO", type="left")
test4(1)
dPO(1)/(1-pPO(0))
if(abs(test4(1)-dPO(1)/(1-pPO(0)))>0.00001) stop("error in left trucation")
test4(1, log=TRUE)
log(dPO(1)/(1-pPO(0)))
if(abs(test4(1, log=TRUE)-log(dPO(1)/(1-pPO(0))))>0.00001)
stop("error in left trucation")
sum(test4(x=1:20, mu=2)) #
sum(test4(x=1:200, mu=80)) #
plot(function(x) test4(x, mu=20), from=1, to=51, n=50+1, type="h") # pdf
# right
# right truncated at 10 means 10 is excluded
test5<-trun.d(par=c(10), family="NBI", type="right")
test5(2)
dNBI(2)/(pNBI(9))
if(abs(test5(1)-dNBI(1)/(pNBI(9)))>0.00001) stop("error in right trucation")
test5(1, log=TRUE)
log(dNBI(1)/(pNBI(9)))
if(abs(test5(1, log=TRUE)-log(dNBI(1)/(pNBI(9))))>0.00001) stop("error in right trucation")
sum(test5(x=0:9, mu=2, sigma=2)) #
sum(test5(x=0:9, mu=300, sigma=5)) # can have mu > parameter
plot(function(x) test5(x, mu=20, sigma=3), from=0, to=9, n=10, type="h") # pdf
plot(function(x) test5(x, mu=300, sigma=5), from=0, to=9, n=10, type="h") # pdf
#----------------------------------------------------------------------------------------
# both
test6<-trun.d(par=c(0,10), family="NBI", type="both")
test6(2)
dNBI(2)/(pNBI(9)-pNBI(0))
if(abs(test6(2)-dNBI(2)/(pNBI(9)-pNBI(0)))>0.00001)
stop("error in right trucation")
test6(1, log=TRUE)
log(dNBI(1)/(pNBI(9)-pNBI(0)))
if(abs(test6(1, log=TRUE)-log(dNBI(1)/(pNBI(9)-pNBI(0))))>0.00001)
stop("error in right trucation")
sum(test6(x=1:9, mu=2, sigma=2)) #
sum(test6(x=1:9, mu=100, sigma=5)) # can have mu > parameter
plot(function(x) test6(x, mu=20, sigma=3), from=1, to=9, n=9, type="h") # pdf
plot(function(x) test6(x, mu=300, sigma=.4), from=1, to=9, n=9, type="h") # pdf
#------------------------------------------------------------------------------------------
# now try when the trucated points varies for each observarion
# this will be appropriate for regression models only
# continuous
#----------------------------------------------------------------------------------------
# left truncation
test7<-trun.d(par=c(0,1,2), family="TF", type="left", varying=TRUE)
test7(c(1,2,3))
dTF(c(1,2,3))/(1-pTF(c(0,1,2)))
test7(c(1,2,3), log=TRUE)
#----------------------------------------------------------------------------------------
# right truncation
test8<-trun.d(par=c(10,11,12), family="BCT", type="right", varying=TRUE)
test8(c(1,2,3))
dBCT(c(1,2,3))/(pBCT(c(10,11,12)))
test8(c(1,2,3), log=TRUE)
#----------------------------------------------------------------------------------------
# both left and right truncation
test9<-trun.d(par=cbind(c(0,1,2),c(10,11,12) ), family="TF", type="both",
varying=TRUE)
test9(c(1,2,3))
dTF(c(1,2,3))/ (pTF(c(10,11,12))-pTF(c(0,1,2)))
test3(c(1,2,3), log=TRUE)
#----------------------------------------------------------------------------------------
# discrete
# left
test10<-trun.d(par=c(0,1,2), family="PO", type="left", varying=TRUE)
test10(c(1,2,3))
dPO(c(1,2,3))/(1-pPO(c(0,1,2)))
# right
test11<-trun.d(par=c(10,11,12), family="NBI", type="right", varying=TRUE)
test11(c(1,2,3))
dNBI(c(1,2,3))/pNBI(c(9,10,11))
# both
test12<-trun.d(par=rbind(c(0,10), c(1,11), c(2,12)), family="NBI", type="both", varying=TRUE)
test12(c(2,3,4))
dNBI(c(2,3,4))/(pNBI(c(9,10,11))-pNBI(c(0,1,2)))
Truncated Cumulative Density Function of a gamlss.family Distribution
Description
Creates a truncated cumulative density function version from a current GAMLSS family distribution.
For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).
Usage
trun.p(par, family = "NO", type = c("left", "right", "both"),
varying = FALSE, ...)
Arguments
par |
a vector with one (for |
family |
a |
type |
whether |
varying |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |
... |
for extra arguments |
Value
Return a p family function
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/).
See Also
trun.d, trun.q, trun.r, gen.trun
Examples
# trucated p continuous function
# continuous
#----------------------------------------------------------------------------------------
# left
test1<-trun.p(par=c(0), family="TF", type="left")
test1(1)
(pTF(1)-pTF(0))/(1-pTF(0))
if(abs(test1(1)-(pTF(1)-pTF(0))/(1-pTF(0)))>0.00001)
stop("error in left trucation of p")
plot(function(x) test1(x, mu=2, sigma=1, nu=2),0,10)
#----------------------------------------------------------------------------------------
# right
test2 <- trun.p(par=c(10), family="BCT", type="right")
test2(1)
pBCT(1)/pBCT(10)
if(abs(test2(1)-pBCT(1)/pBCT(10))>0.00001) stop("error in right trucation")
test2(1, lower.tail=FALSE)
1-pBCT(1)/pBCT(10)
if(abs(test2(1, lower.tail=FALSE)-(1-pBCT(1)/pBCT(10)))>0.00001)
stop("error in right trucation")
test2(1, log.p=TRUE)
log(pBCT(1)/pBCT(10))
if(abs(test2(1, log.p=TRUE)-log(pBCT(1)/pBCT(10)))>0.00001)
stop("error in right trucation")
plot(function(x) test2(x, mu=2, sigma=1, nu=2, tau=2),0,10)
plot(function(x) test2(x, mu=2, sigma=1, nu=2, tau=2,
lower.tail=FALSE),0,10)
#----------------------------------------------------------------------------------------
# both
test3<-trun.p(par=c(-3,3), family="TF", type="both")
test3(1)
(pTF(1)-pTF(-3))/(pTF(3)-pTF(-3))
if(abs(test3(1)-(pTF(1)-pTF(-3))/(pTF(3)-pTF(-3)))>0.00001)
stop("error in right trucation")
test3(1, lower.tail=FALSE)
1-(pTF(1)-pTF(-3))/(pTF(3)-pTF(-3))
if(abs(test3(0,lower.tail=FALSE)-
(1-(pTF(0)-pTF(-3))/(pTF(3)-pTF(-3))))>0.00001)
stop("error in right trucation")
plot(function(x) test3(x, mu=2, sigma=1, nu=2, ),-3,3)
plot(function(x) test3(x, mu=2, sigma=1, nu=2, lower.tail=FALSE),-3,3)
#----------------------------------------------------------------------------------------
# Discrete
#----------------------------------------------------------------------------------------
# trucated p function
# left
test4<-trun.p(par=c(0), family="PO", type="left")
test4(1)
(pPO(1)-pPO(0))/(1-pPO(0))
if(abs(test4(1)-(pPO(1)-pPO(0))/(1-pPO(0)))>0.00001)
stop("error in left trucation of p")
plot(function(x) test4(x, mu=2), from=1, to=10, n=10, type="h")
cdf <- stepfun(1:40, test4(1:41, mu=5), f = 0)
plot(cdf, main="cdf", ylab="cdf(x)", do.points=FALSE )
#----------------------------------------------------------------------------------------
# right
test5<-trun.p(par=c(10), family="NBI", type="right")
test5(2)
pNBI(2)/(pNBI(9))
if(abs(test5(2)-(pNBI(2)/(pNBI(9))))>0.00001)
stop("error in right trucation of p")
plot(function(x) test5(x, mu=2), from=0, to=9, n=10, type="h")
cdf <- stepfun(0:8, test5(0:9, mu=5), f = 0)
plot(cdf, main="cdf", ylab="cdf(x)", do.points=FALSE )
#----------------------------------------------------------------------------------------
# both
test6<-trun.p(par=c(0,10), family="NBI", type="both")
test6(2)
(pNBI(2)-pNBI(0))/(pNBI(9)-pNBI(0))
if(abs(test6(2)-(pNBI(2)-pNBI(0))/(pNBI(9)-pNBI(0)))>0.00001)
stop("error in the both trucation")
test6(1, log=TRUE)
log((pNBI(1)-pNBI(0))/(pNBI(9)-pNBI(0)))
if(abs(test6(1, log=TRUE)-log((pNBI(1)-pNBI(0))/(pNBI(9)-pNBI(0))))>0.00001)
stop("error in both trucation")
plot(function(y) test6(y, mu=20, sigma=3), from=1, to=9, n=9, type="h")
plot(function(y) test6(y, mu=300, sigma=.4), from=1, to=9, n=9, type="h")
cdf <- stepfun(1:8, test6(1:9, mu=5), f = 0)
plot(cdf, main="cdf", ylab="cdf(x)", do.points=FALSE )
#----------------------------------------------------------------------------------------
# varying truncation
#----------------------------------------------------------------------------------------
# coninuous
# left
test6<-trun.p(par=c(0,1,2), family="TF", type="left", varying=TRUE)
test6(c(2,3,4))
(pTF(c(2,3,4))-pTF(c(0,1,2)))/(1-pTF(c(0,1,2)))
test6(c(2,3,4), log.p=TRUE)
#----------------------------------------------------------------------------------------
# right
test7 <- trun.p(par=c(10,11,12), family="BCT", type="right", varying=TRUE)
test7(c(1,2,3))
pBCT(c(1,2,3))/pBCT(c(10,11,12))
test7(c(1,2,3), lower.tail=FALSE)
1-pBCT(c(1,2,3))/pBCT(c(10,11,12))
test7(c(1,2,3), log.p=TRUE)
#---------------------------------------------------------------------------------------
# both
test8<-trun.p(par=cbind(c(0,1,2), c(10,11,12)), family="TF",
type="both", varying=TRUE)
test8(c(1,2,3))
(pTF(c(1,2,3))-pTF(c(0,1,2)))/(pTF(c(10,11,12))-pTF(c(0,1,2)))
test8(c(1,2,3), lower.tail=FALSE)
1-(pTF(c(1,2,3))-pTF(c(0,1,2)))/(pTF(c(10,11,12))-pTF(c(0,1,2)))
#--------------------------------------------------------------------------------------
# discrete
#--------------------------------------------------------------------------------------
# left
test9<-trun.p(par=c(0,1,2), family="PO", type="left", varying=TRUE)
test9(c(1,2,3))
(pPO(c(1,2,3))-pPO(c(0,1,2)))/(1-pPO(c(0,1,2)))
#--------------------------------------------------------------------------------------
# right
test10<-trun.p(par=c(10,11,12), family="NBI", type="right", varying=TRUE)
test10(c(2,3,4))
pNBI(c(2,3,4))/(pNBI(c(9,10,11)))
#-------------------------------------------------------------------------------------
# both
test11<-trun.p(par=rbind(c(0,10), c(1,11), c(2, 12)), family="NBI",
type="both", varying=TRUE)
test11(c(2,3,4))
(pNBI(c(2,3,4))-pNBI(c(0,1,2)))/(pNBI(c(9,10,11))-pNBI(c(0,1,2)))
#-------------------------------------------------------------------------------------
Truncated Inverse Cumulative Density Function of a gamlss.family Distribution
Description
Creates a function to produce the inverse of a truncated cumulative density function generated from a current GAMLSS family distribution.
For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).
Usage
trun.q(par, family = "NO", type = c("left", "right", "both"),
varying = FALSE, ...)
Arguments
par |
a vector with one (for |
family |
a |
type |
whether |
varying |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |
... |
for extra arguments |
Value
Returns a q family function
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/)..
See Also
trun.d, trun.q, trun.r, gen.trun
Examples
# trucated q continuous function
# continuous
#----------------------------------------------------------------------------------------
# left
test1<-trun.q(par=c(0), family="TF", type="left")
test1(.6)
qTF(pTF(0)+0.6*(1-pTF(0)))
#----------------------------------------------------------------------------------------
# right
test2 <- trun.q(par=c(10), family="BCT", type="right")
test2(.6)
qBCT(0.6*pBCT(10))
#----------------------------------------------------------------------------------------
# both
test3<-trun.q(par=c(-3,3), family="TF", type="both")
test3(.6)
qTF(0.6*(pTF(3)-pTF(-3))+pTF(-3))
#----------------------------------------------------------------------------------------
# varying par
#----------------------------------------------------------------------------------------
# left
test7<-trun.q(par=c(0,1,2), family="TF", type="left", varying=TRUE)
test7(c(.5,.5,.6))
qTF(pTF(c(0,1,2))+c(.5,.5,.6)*(1-pTF(c(0,1,2))))
#---------------------------------------------------------------------------------------
# right
test9 <- trun.q(par=c(10,11,12), family="BCT", type="right", varying=TRUE)
test9(c(.5,.5,.6))
qBCT(c(.5,.5,.6)*pBCT(c(10,11,12)))
#----------------------------------------------------------------------------------------
# both
test10<-trun.q(par=cbind(c(0,1,2), c(10,11,12)), family="TF", type="both", varying=TRUE)
test10(c(.5, .5, .7))
qTF(c(.5, .5, .7)*(pTF(c(10,11,12))-pTF(c(0,1,2)))+pTF(c(0,1,2)))
#----------------------------------------------------------------------------------------
# FOR DISCRETE DISTRIBUTIONS
# trucated q function
# left
test4<-trun.q(par=c(0), family="PO", type="left")
test4(.6)
qPO(pPO(0)+0.6*(1-pPO(0)))
# varying
test41<-trun.q(par=c(0,1,2), family="PO", type="left", varying=TRUE)
test41(c(.6,.4,.5))
qPO(pPO(c(0,1,2))+c(.6,.4,.5)*(1-pPO(c(0,1,2))))
#----------------------------------------------------------------------------------------
# right
test5 <- trun.q(par=c(10), family="NBI", type="right")
test5(.6)
qNBI(0.6*pNBI(10))
test5(.6, mu=10, sigma=2)
qNBI(0.6*pNBI(10, mu=10, sigma=2), mu=10, sigma=2)
# varying
test51 <- trun.q(par=c(10, 11, 12), family="NBI", type="right", varying=TRUE)
test51(c(.6,.4,.5))
qNBI(c(.6,.4,.5)*pNBI(c(10, 11, 12)))
test51(c(.6,.4,.5), mu=10, sigma=2)
qNBI(c(.6,.4,.5)*pNBI(c(10, 11, 12), mu=10, sigma=2), mu=10, sigma=2)
#----------------------------------------------------------------------------------------
# both
test6<-trun.q(par=c(0,10), family="NBI", type="both")
test6(.6)
qNBI(0.6*(pNBI(10)-pNBI(0))+pNBI(0))
# varying
test61<-trun.q(par=cbind(c(0,1,2), c(10,11,12)), family="NBI", type="both", varying=TRUE)
test61(c(.6,.4,.5))
qNBI(c(.6,.4,.5)*(pNBI(c(10,11,12))-pNBI(c(0,1,2)))+pNBI(c(0,1,2)))
#----------------------------------------------------------------------------------------
Generates Random Values from a Truncated Density Function of a gamlss.family Distribution
Description
Creates a function to generate randon values from a truncated probability density function created from a current GAMLSS family distribution
For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).
Usage
trun.r(par, family = "NO", type = c("left", "right", "both"),
varying = FALSE, ...)
Arguments
par |
a vector with one (for |
family |
a |
type |
whether |
varying |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |
... |
for extra arguments |
Value
Returns a r family function
Author(s)
Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk and Bob Rigby
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. 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/).
See Also
trun.p, trun.q, trun.d, gen.trun
Examples
# trucated r function
# continuous
#----------------------------------------------------------------------------------------
# left
test1<-trun.r(par=c(0), family="TF", type="left")
rr<-test1(1000)
hist(rr)
#----------------------------------------------------------------------------------------
# right
test2 <- trun.r(par=c(10), family="BCT", type="right")
rr<-test2(1000)
hist(rr)
#----------------------------------------------------------------------------------------
# both
test3<-trun.r(par=c(-3,3), family="TF", type="both")
rr<-test3(1000)
hist(rr)
#----------------------------------------------------------------------------------------
# discrete
# trucated r function
# left
test4<-trun.r(par=c(0), family="PO", type="left")
tN <- table(Ni <- test4(1000))
r <- barplot(tN, col='lightblue')
#----------------------------------------------------------------------------------------
# right
test5 <- trun.r(par=c(10), family="NBI", type="right")
tN <- table(Ni <- test5(1000))
r <- barplot(tN, col='lightblue')
tN <- table(Ni <- test5(1000,mu=5))
r <- barplot(tN, col='lightblue')
tN <- table(Ni <- test5(1000,mu=10, sigma=.1))
r <- barplot(tN, col='lightblue')
#----------------------------------------------------------------------------------------
# both
test6<-trun.r(par=c(0,10), family="NBI", type="both")
tN <- table(Ni <- test6(1000,mu=5))
r <- barplot(tN, col='lightblue')
#----------------------------------------------------------------------------------------
# varying = TRUE
#----------------------------------------------------------------------------------------
# continuous
#----------------------------------------------------------------------------------------
# left
test7<-trun.r(par=c(0,1,2), family="TF", type="left", varying=TRUE)
test7(3)
#----------------------------------------------------------------------------------------
# right
test8 <- trun.r(par=c(10,11,12), family="BCT", type="right", varying=TRUE)
test8(3)
#----------------------------------------------------------------------------------------
# both
test9<-trun.r(par=rbind(c(-3,3), c(-1,5), c(0,6)), , family="TF", type="both", varying=TRUE)
test9(3)
#----------------------------------------------------------------------------------------
# discrete
# trucated r function
# left
test10<-trun.r(par=c(0,1,2), family="PO", type="left", varying=TRUE)
test10(3)
#----------------------------------------------------------------------------------------
# right
test11 <- trun.r(par=c(10,11,12), family="NBI", type="right", varying=TRUE)
test11(3)
test11(3, mu=10, sigma=.1)
#----------------------------------------------------------------------------------------
# both
test12<-trun.r(par=rbind(c(0,10), c(1,11), c(2,12)), family="NBI", type="both", varying=TRUE)
test12(3,mu=5)