trun.d: Truncated Probability Density Function of a gamlss.family...
In gamlss.tr: Generating and Fitting Truncated `gamlss.family' Distributions
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
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
1
2
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 mikis.stasinopoulos@gamlss.org 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.
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/).
See Also
trun.p, trun.q, trun.r, gen.trun
Examples
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#------------------------------------------------------------------------------------------
# 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)))
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Attaching package: ‘gamlss.data’
The following object is masked from ‘package:datasets’:
sleep
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.2-0 **********
For more on GAMLSS look at https://www.gamlss.com/
Type gamlssNews() to see new features/changes/bug fixes.
[1] 0.460724
[1] 0.460724
[1] -0.7749562
[1] -0.7749562
1 with absolute error < 8.9e-10
1 with absolute error < 1.9e-05
1 with absolute error < 5e-06
[1] 0.003767161
[1] 0.003767161
[1] -5.581434
[1] -5.581434
1 with absolute error < 4.4e-05
1 with absolute error < 1.7e-07
1 with absolute error < 5.3e-07
[1] 0.3943707
[1] 0.3943707
[1] -0.9304639
[1] -0.9304639
1 with absolute error < 2.9e-05
[1] 0.5819767
[1] 0.5819767
[1] -0.5413249
[1] -0.5413249
[1] 1
[1] 1
[1] 0.1251222
[1] 0.1251222
[1] -1.385317
[1] -1.385317
[1] 1
[1] 1
[1] 0.2504892
[1] 0.2504892
[1] -0.6911921
[1] -0.6911921
[1] 1
[1] 1
[1] 0.4607240 0.3587386 0.3106923
[1] 0.4607240 0.3587386 0.3106923
[1] -0.7749562 -1.0251612 -1.1689522
[1] 0.003767161 0.008609972 0.026385923
[1] 0.003767161 0.008609972 0.026385923
[1] -5.581434 -4.754834 -3.634925
[1] 0.4607247 0.3587393 0.3106936
[1] 0.4607247 0.3587393 0.3106936
[1] -1.454670 -2.781061 -4.460660
[1] 0.5819767 0.6961056 0.7635389
[1] 0.5819767 0.6961056 0.7635389
[1] 0.25024438 0.12506106 0.06251526
[1] 0.25024438 0.12506106 0.06251526
[1] 0.2504892 0.2504892 0.2504892
[1] 0.2504892 0.2504892 0.2504892
gamlss.tr documentation built on July 13, 2020, 5:07 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Value Author(s) References See Also Examples
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
1 2 |
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 mikis.stasinopoulos@gamlss.org 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.
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/).
See Also
trun.p, trun.q, trun.r, gen.trun
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 | #------------------------------------------------------------------------------------------
# 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)))
|
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Attaching package: ‘gamlss.data’
The following object is masked from ‘package:datasets’:
sleep
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.2-0 **********
For more on GAMLSS look at https://www.gamlss.com/
Type gamlssNews() to see new features/changes/bug fixes.
[1] 0.460724
[1] 0.460724
[1] -0.7749562
[1] -0.7749562
1 with absolute error < 8.9e-10
1 with absolute error < 1.9e-05
1 with absolute error < 5e-06
[1] 0.003767161
[1] 0.003767161
[1] -5.581434
[1] -5.581434
1 with absolute error < 4.4e-05
1 with absolute error < 1.7e-07
1 with absolute error < 5.3e-07
[1] 0.3943707
[1] 0.3943707
[1] -0.9304639
[1] -0.9304639
1 with absolute error < 2.9e-05
[1] 0.5819767
[1] 0.5819767
[1] -0.5413249
[1] -0.5413249
[1] 1
[1] 1
[1] 0.1251222
[1] 0.1251222
[1] -1.385317
[1] -1.385317
[1] 1
[1] 1
[1] 0.2504892
[1] 0.2504892
[1] -0.6911921
[1] -0.6911921
[1] 1
[1] 1
[1] 0.4607240 0.3587386 0.3106923
[1] 0.4607240 0.3587386 0.3106923
[1] -0.7749562 -1.0251612 -1.1689522
[1] 0.003767161 0.008609972 0.026385923
[1] 0.003767161 0.008609972 0.026385923
[1] -5.581434 -4.754834 -3.634925
[1] 0.4607247 0.3587393 0.3106936
[1] 0.4607247 0.3587393 0.3106936
[1] -1.454670 -2.781061 -4.460660
[1] 0.5819767 0.6961056 0.7635389
[1] 0.5819767 0.6961056 0.7635389
[1] 0.25024438 0.12506106 0.06251526
[1] 0.25024438 0.12506106 0.06251526
[1] 0.2504892 0.2504892 0.2504892
[1] 0.2504892 0.2504892 0.2504892
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