# 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

1 2 3 4 5 |

### 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 |

### 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.

### See Also

`gamlss.family`

, `LOGNO`

### Examples

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)
``` |