Functions to generate log and logit distributions from existing continuous gamlss.family distributions
There are five functions here. Only the functions Family
and gen.Family
should be used (see details).
Family.d(family = "NO", type = c("log", "logit"), ...) Family.p(family = "NO", type = c("log", "logit"), ...) Family.q(family = "NO", type = c("log", "logit"), ...) Family.r(family = "NO", type = c("log", "logit"), ...) Family(family = "NO", type = c("log", "logit"), local = TRUE, ...) gen.Family(family = "NO", type = c("log", "logit"), ...)
family |
a continuous |
type |
the type of transformation only "log" and "logit" are allowed |
local |
It is TRUE if is called within |
... |
for passing extra arguments |
The function gen.Family
creates the standard d,p,q,r
functions for the distribution plus the fitting gamlss.family
. For example gen.Family("NO", "logit")
will generate the functions
dlogitNO()
, plogitNO()
, qlogitNO()
, rlogitNO()
and dlogitNO()
.
The latest function can be used in family
argument of gamlss()
to fit a logic-Normal distribution i.e. family=logitNO
.
The same fitting can be achieved by using family=Family("NO", "logit")
. Here the required dlogitNO()
, plogitNO()
and
logitNO()
functions are generated locally within the gamlss()
environment.
The function gen.Family
returns the d
, p
, q
r
functions plus the fitting function.
Mikis Stasinopoulos and Bob Rigby
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.
# generating a log t distribution gen.Family("TF") # plotting the d, p, q, and r functions op<-par(mfrow=c(2,2)) curve(dlogTF(x, mu=0), 0, 10) curve(plogTF(x, mu=0), 0, 10) curve(qlogTF(x, mu=0), 0, 1) Y<- rlogTF(200) hist(Y) par(op) # different mu curve(dlogTF(x, mu=-1, sigma=1, nu=10), 0, 5, ylim=c(0,1)) curve(dlogTF(x, mu=0, sigma=1, nu=10), 0, 5, add=TRUE, col="red", lty=2) curve(dlogTF(x, mu=1, sigma=1, nu=10), 0, 5, add=TRUE, col="blue", lty=3) # different sigma curve(dlogTF(x, mu=0, sigma=.5, nu=10), 0, 5, ylim=c(0,1)) curve(dlogTF(x, mu=0, sigma=1, nu=10), 0, 5, add=TRUE, col="red", lty=2) curve(dlogTF(x, mu=0, sigma=2, nu=10), 0, 5, add=TRUE, col="blue", lty=3) # different degrees of freedom nu curve(dlogTF(x, mu=0, sigma=1, nu=1), 0, 5, ylim=c(0,.8), n = 1001) curve(dlogTF(x, mu=0, sigma=1, nu=2), 0, 5, add=TRUE, col="red", lty=2) curve(dlogTF(x, mu=0, sigma=1, nu=5), 0, 5, add=TRUE, col="blue", lty=3) # generating a logit t distribution gen.Family("TF", "logit") # plotting the d, p, q, and r functions op<-par(mfrow=c(2,2)) curve(dlogitTF(x, mu=0), 0, 1) curve(plogitTF(x, mu=0), 0, 1) curve(qlogitTF(x, mu=0), 0, 1) abline(v=1) Y<- rlogitTF(200) hist(Y) par(op) # different mu curve(dlogitTF(x, mu=-2, sigma=1, nu=10), 0, 1, ylim=c(0,5)) curve(dlogitTF(x, mu=0, sigma=1, nu=10), 0, 1, add=TRUE, col="red", lty=2) curve(dlogitTF(x, mu=2, sigma=1, nu=10), 0, 1, add=TRUE, col="blue", lty=3) # different sigma curve(dlogitTF(x, mu=0, sigma=1, nu=10), 0, 1, ylim=c(0,2.5)) curve(dlogitTF(x, mu=0, sigma=2, nu=10), 0, 1, add=TRUE, col="red", lty=2) curve(dlogitTF(x, mu=0, sigma=.7, nu=10), 0, 1, add=TRUE, col="blue", lty=3) # different degrees of freedom nu curve(dlogitTF(x, mu=0, sigma=1, nu=1), 0, 1, ylim=c(0,1.6)) curve(dlogitTF(x, mu=0, sigma=1, nu=2), 0, 1, add=TRUE, col="red", lty=2) curve(dlogitTF(x, mu=0, sigma=1, nu=5), 0, 1, add=TRUE, col="blue", lty=3)
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