RBS: Reparameterized Birnbaum-Saunders (RBS) distribution for...

In santosneto/RBS: Regression models for Birnbaum-Saunders distributions

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

RBS(mu.link = "log", sigma.link = "log")

sigmatil(y)

Ims(mu, sigma)

resrbs(y, mu, sigma)

dRBS(x, mu = 1, sigma = 1, log = FALSE)

pRBS(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qRBS(p, mu = 0.5, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rRBS(n, mu = 1, sigma = 1)

plotRBS(
  mu = 0.5,
  sigma = 1,
  from = 0,
  to = 0.999,
  n = 101,
  title = "title",
  ...
)

meanRBS(obj)

est.rbs(x, xi = 0.95)

Arguments

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

Details

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

f_{Y}(y;μ,σ)=\frac{\exp≤ft(σ/2\right)√{σ+1}}{4√{πμ}\,y^{3/2}} ≤ft[y+\frac{σ μ}{σ+1}\right] \exp≤ft(-\frac{σ}{4} ≤ft[\frac{y\{σ+1\}}{σμ}+\frac{σμ}{y\{σ+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 [e-mail], F.J.A. Cysneiros [e-mail], Victor Leiva [e-mail] and Michelli Barros [e-mail]

References

Santos-Neto, M., Cysneiros, F.J.A, Leiva, V., Barros, M. (2012) On new parameterizations of the Birnbaum-Saunders distribution. PAK J STAT, v. 28, p. 1-26, 2012.

Santos-Neto, M., Cysneiros, F.J.A, Leiva, V., Barros, M. (2014) On a reparameterized Birnbaum-Saunders distribution and its moments, estimation and application. Revstat Statistical Journal, v. 12, p. 247-272, 2014.

Leiva, V., Santos-Neto, M., Cysneiros, F.J.A, Barros, M. (2014) Birnbaum-Saunders statistical modelling: a new approach. Statistical Modelling, v. 14, p. 21-48, 2014.

Examples

data(cpd,package='faraway')
attach(cpd)
model0 = gamlss::gamlss(actual ~ projected, family=RBS(mu.link="identity"),method=CG())
summary(model0)
model = gamlss::gamlss(actual ~ 0+projected, family=RBS(mu.link="identity"),method=CG())
summary(model)

santosneto/RBS documentation built on Feb. 5, 2021, 2:12 p.m.