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Last data update: 2014.03.03

R: Truncated Probability Density Function of a gamlss.family...

trun.d

R Documentation

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 `"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

Value

Returns a d family function

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk and Bob Rigby r.rigby@londonmet.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.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2003) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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)))