# rRBS: Reparameterized Birnbaum-Saunders (RBS) distribution for... In santosneto/rbsmodels: Reparameterized Birnbaum-Saunders regression model

## Description

The fuction RBS() defines the BS distribution, a two paramenter distribution, for a gamlss.family object to be used in GAMLSS fitting using using the function gamlss(), with mean equal to the parameter mu and sigma equal the precision parameter. The functions dRBS, pRBS, qRBS and rBS define the density, distribution function, quantile function and random genetation for the RBS parameterization of the RBS distribution.

## Usage

 1 2 3 4 5 6 7 RBS(mu.link = "identity", sigma.link = "identity") dRBS(x, mu = 1, sigma = 1, log = FALSE) pRBS(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE) qRBS(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE) rRBS(n, mu = 1, sigma = 1) plotRBS(mu = .5, sigma = 1, from = 0, to = 0.999, n = 101, ...) meanRBS(obj) 

## Arguments

 n number of observations. If length(n) > 1, the length is taken to be the number required. mu vector of scale parameter values sigma vector of shape parameter values mu.link object for which the extraction of model residuals is meaningful. sigma.link type of residual to be used. x, q vector of quantiles 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. from where to start plotting the distribution from to up to where to plot the distribution obj a fitted RBS object ... other graphical parameters for plotting

## Details

The parametrization of the normal distribution given in the function RBS() is

f_{Y}(y;μ,δ)=\frac{\exp≤ft(δ/2\right)√{δ+1}}{4√{πμ}\,y^{3/2}} ≤ft[y+\frac{δ μ}{δ+1}\right] \exp≤ft(-\frac{δ}{4} ≤ft[\frac{y\{δ+1\}}{δμ}+\frac{δμ}{y\{δ+1\}}\right]\right) y>0.

## Value

returns a gamlss.family object which can be used to fit a normal distribution in the gamlss() function.

## Note

For the function RBS(), mu is the mean and sigma is the precision parameter of the Birnbaum-Saunders distribution.

## Author(s)

Manoel Santos-Neto [email protected], F.J.A. Cysneiros [email protected], Victor Leiva [email protected] and Michelli Barros [email protected]

## Examples

 1 2 3 4 plotRBS() dat <- rRBS(1000); hist(dat) fit <- gamlss(dat~1,family=RBS(),method=CG()) meanRBS(fit) 

santosneto/rbsmodels documentation built on May 26, 2017, 12:32 a.m.