R: Logarithmic and zero adjusted logarithmic distributions for...

LG {gamlss.dist} | R Documentation

## Logarithmic and zero adjusted logarithmic distributions for fitting a GAMLSS model

### Description

The function `LG` defines the logarithmic distribution, a one parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dLG`, `pLG`, `qLG` and `rLG` define the density, distribution function, quantile function and random generation for the logarithmic , `LG()`, distribution.

The function `ZALG` defines the zero adjusted logarithmic distribution, a two parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZALG`, `pZALG`, `qZALG` and `rZALG` define the density, distribution function, quantile function and random generation for the inflated logarithmic , `ZALG()`, distribution.

### Usage

    LG(mu.link = "logit")
    dLG(x, mu = 0.5, log = FALSE)
    pLG(q, mu = 0.5, lower.tail = TRUE, log.p = FALSE)
    qLG(p, mu = 0.5, lower.tail = TRUE, log.p = FALSE, max.value = 10000)
    rLG(n, mu = 0.5)
    ZALG(mu.link = "logit", sigma.link = "logit")
    dZALG(x, mu = 0.5, sigma = 0.1, log = FALSE)
    pZALG(q, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    qZALG(p, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    rZALG(n, mu = 0.5, sigma = 0.1)

### Arguments

`mu.link` | defines the `mu.link`, with `logit` link as the default for the `mu` parameter
`sigma.link` | defines the `sigma.link`, with `logit` link as the default for the sigma parameter which in this case is the probability at zero.
`x` | vector of (non-negative integer)
`mu` | vector of positive means
`sigma` | vector of probabilities at zero
`p` | vector of probabilities
`q` | vector of quantiles
`n` | number of random values to return
`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]
`max.value` | valued needed for the numerical calculation of the q-function

### Details

For the definition of the distributions see Rigby and Stasinopoulos (2010) below.

The parameterization of the logarithmic distribution in the function `LM` is

f(y|mu) = α μ^y / y

where for y>=1 and μ>0 and

α= [log(1-μ)]^{-1}

### Value

The function `LG` and `ZALG` return a `gamlss.family` object which can be used to fit a logarithmic and a zero inflated logarithmic distributions respectively in the `gamlss()` function.

### Author(s)

Mikis Stasinopoulos, Bob Rigby

### References

Johnson, Norman Lloyd; Kemp, Adrienne W; Kotz, Samuel (2005). "Chapter 7: Logarithmic and Lagrangian distributions". Univariate discrete distributions (3 ed.). John Wiley & Sons. ISBN 9780471272465.

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.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see https://www.gamlss.com/)

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`, `PO`, `ZAP`

### Examples

    LG()
    ZAP()
    # creating data and plotting them
     dat <- rLG(1000, mu=.3)
       r <- barplot(table(dat), col='lightblue')
    dat1 <- rZALG(1000, mu=.3, sigma=.1)
      r1 <- barplot(table(dat1), col='lightblue')

[Package gamlss.dist version 5.3-2 Index]