gamlss.tr (version 5.1-9)

trun.q: 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, ...)

Value

Returns a q family function

Arguments

par

a vector with one (for "left" or "right" truncation) or two elements for "both". When the argument varying = TRUE then par can be a vector or a matrix with two columns respectively.

family

a gamlss.family object, which is used to define the distribution and the link functions of the various parameters. The distribution families supported by gamlss() can be found in gamlss.family. Functions such as BI() (binomial) produce a family object.

type

whether left, right or in both sides truncation is required, (left is the default)

varying

whether the truncation varies for diferent observations. This can be usefull in regression analysis. If varying = TRUE then par should be an n-length vector for type equal "left" and "right" and an n by 2 matrix for type="both"

...

for extra arguments

Author

Mikis Stasinopoulos 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)))
#----------------------------------------------------------------------------------------