The functions `PARETO2()`

and `PARETO2o()`

define the Pareto Type 2 distribution, a two parameter distribution, for a `gamlss.family`

object to be used in GAMLSS fitting using the function `gamlss()`

.
The parameters are `mu`

and `sigma`

in both functions but the parameterasation different. The `mu`

is identical for both `PARETO2()`

and `PARETO2o()`

. The `sigma`

in `PARETO2o()`

is the inverse of the `sigma`

in codePARETO2() and coresponse to the usual parameter `alpha`

of the Patreto distribution. The functions `dPARETO2`

, `pPARETO2`

, `qPARETO2`

and `rPARETO2`

define the density, distribution function, quantile function and random generation for the `PARETO2`

parameterization of the Pareto type 2 distribution while the functions `dPARETO2o`

, `pPARETO2o`

, `qPARETO2o`

and `rPARETO2o`

define the density, distribution function, quantile function and random generation for the original `PARETO2o`

parameterization of the Pareto type 2 distribution

1 2 3 4 5 6 7 8 9 10 | ```
PARETO2(mu.link = "log", sigma.link = "log")
dPARETO2(x, mu = 1, sigma = 0.5, log = FALSE)
pPARETO2(q, mu = 1, sigma = 0.5, lower.tail = TRUE, log.p = FALSE)
qPARETO2(p, mu = 1, sigma = 0.5, lower.tail = TRUE, log.p = FALSE)
rPARETO2(n, mu = 1, sigma = 0.5)
PARETO2o(mu.link = "log", sigma.link = "log")
dPARETO2o(x, mu = 1, sigma = 0.5, log = FALSE)
pPARETO2o(q, mu = 1, sigma = 0.5, lower.tail = TRUE, log.p = FALSE)
qPARETO2o(p, mu = 1, sigma = 0.5, lower.tail = TRUE, log.p = FALSE)
rPARETO2o(n, mu = 1, sigma = 0.5)
``` |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`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 |

The parameterization of the Pareto Type 2 distribution in the function `PA2`

is:

*f(y|mu, sigma) = (1/sigma) mu^(1/sigma) (y+mu)^(-(1/sigma+1))*

for *y>=0*, *mu>0* and *sigma>0*.

returns a gamlss.family object which can be used to fit a Pareto type 2 distribution in the `gamlss()`

function.

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos

Johnson, N., Kotz, S., and Balakrishnan, N. (1997). *Discrete Multivariate
Distributions.* Wiley-Interscience, NY, USA.

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.

`gamlss.family`

1 2 3 4 5 6 7 8 9 10 |

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