NO | R Documentation |

The function `NO()`

defines the normal distribution, a two parameter distribution, for a
`gamlss.family`

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

, with mean equal to the parameter `mu`

and `sigma`

equal the standard deviation.
The functions `dNO`

, `pNO`

, `qNO`

and `rNO`

define the density, distribution function, quantile function and random
generation for the `NO`

parameterization of the normal distribution.
[A alternative parameterization with `sigma`

equal to the variance is given in the function `NO2()`

]

NO(mu.link = "identity", sigma.link = "log") dNO(x, mu = 0, sigma = 1, log = FALSE) pNO(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qNO(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rNO(n, mu = 0, sigma = 1)

`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 parametrization of the normal distribution given in the function `NO()`

is

*f(y|mu,sigma)=(1/(sqrt(2*pi)*sigma))* exp(-0.5*((y-mu)/sigma)^2)*

for *y=(-Inf,+Inf)*, *μ=(-Inf,+Inf)* and *σ>0* see pp. 369-370 of Rigby et al. (2019).

returns a `gamlss.family`

object which can be used to fit a normal distribution in the `gamlss()`

function.

For the function `NO()`

, *mu* is the mean and *sigma* is the standard deviation (not the variance) of the normal distribution.

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

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, doi: 10.1201/9780429298547. 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, doi: 10.18637/jss.v023.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. doi: 10.1201/b21973

(see also https://www.gamlss.com/).

`gamlss.family`

, `NO2`

NO()# gives information about the default links for the normal distribution plot(function(y) dNO(y, mu=10 ,sigma=2), 0, 20) plot(function(y) pNO(y, mu=10 ,sigma=2), 0, 20) plot(function(y) qNO(y, mu=10 ,sigma=2), 0, 1) dat<-rNO(100) hist(dat) # library(gamlss) # gamlss(dat~1,family=NO) # fits a constant for mu and sigma

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