Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 8 9 10 | ```
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)
``` |

`mu.link` |
defines the |

`sigma.link` |
defines the |

`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 |

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}*

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.

Mikis Stasinopoulos, Bob Rigby

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 http://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, http://www.jstatsoft.org/v23/i07.

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

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