LOGITNO: Logit Normal distribution for fitting in GAMLSS In mstasinopoulos/GAMLSS-Distibutions: Distributions for Generalized Additive Models for Location Scale and Shape

Description

The functions `dLOGITNO`, `pLOGITNO`, `qLOGITNO` and `rLOGITNO` define the density, distribution function, quantile function and random generation for the logit-normal distribution. The function `LOGITNO` can be used for fitting the distribution in `gamlss()`.

Usage

 ```1 2 3 4 5``` ```LOGITNO(mu.link = "logit", sigma.link = "log") dLOGITNO(x, mu = 0.5, sigma = 1, log = FALSE) pLOGITNO(q, mu = 0.5, sigma = 1, lower.tail = TRUE, log.p = FALSE) qLOGITNO(p, mu = 0.5, sigma = 1, lower.tail = TRUE, log.p = FALSE) rLOGITNO(n, mu = 0.5, sigma = 1) ```

Arguments

 `mu.link` the link function for mu `sigma.link` the link function for sigma `x,q` vector of quantiles `mu` vector of location parameter values `sigma` vector of scale parameter values `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required

Details

The probability density function in `LOGITNO` is defined as

f(y|mu,sigma)=(1/(y*(1-y)*sqrt(2*pi)*sigma))*exp(-0.5*((log(y/(1-y))-log(mu/(1-mu))/(sigma))^2)

for 0<y>1, mu=(0,1) and σ>0.

Value

`LOGITNO()` returns a `gamlss.family` object which can be used to fit a logit-normal distribution in the `gamlss()` function.

Author(s)

Mikis Stasinopoulos, 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. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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, http://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.

`gamlss.family`, `LOGNO`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# plotting the d, p, q, and r functions op<-par(mfrow=c(2,2)) curve(dLOGITNO(x), 0, 1) curve(pLOGITNO(x), 0, 1) curve(qLOGITNO(x), 0, 1) Y<- rLOGITNO(200) hist(Y) par(op) # plotting the d, p, q, and r functions # sigma 3 op<-par(mfrow=c(2,2)) curve(dLOGITNO(x, sigma=3), 0, 1) curve(pLOGITNO(x, sigma=3), 0, 1) curve(qLOGITNO(x, sigma=3), 0, 1) Y<- rLOGITNO(200, sigma=3) hist(Y) par(op) ```