R: Logit Normal distribution for fitting in GAMLSS

LOGITNO {gamlss.dist} | R Documentation

## Logit Normal distribution for fitting in GAMLSS

### 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

    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.

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

`gamlss.family`, `LOGNO`

### Examples

    # 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)

[Package gamlss.dist version 5.3-2 Index]