GB1 creates a gamlss.family object which can be used to fit the distribution using the function
gamlss(). Note the range of the response variable is from zero to one.
The functions dGB1,
GB1, qGB1 and rGB1 define the density,
distribution function, quantile function and random
generation for the generalized beta type 1 distribution.GB1(mu.link = "logit", sigma.link = "logit", nu.link = "log",
tau.link = "log")
dGB1(x, mu = 0.5, sigma = 0.4, nu = 1, tau = 1, log = FALSE)
pGB1(q, mu = 0.5, sigma = 0.4, nu = 1, tau = 1, lower.tail = TRUE,
log.p = FALSE)
qGB1(p, mu = 0.5, sigma = 0.4, nu = 1, tau = 1, lower.tail = TRUE,
log.p = FALSE)
rGB1(n, mu = 0.5, sigma = 0.4, nu = 1, tau = 1)mu.link, with "identity" link as the default for the mu parameter.sigma.link, with "log" link as the default for the sigma parameter.nu.link, with "log" link as the default for the nu parameter.tau.link, with "log" link as the default for the tau parameter.nu parameter valuestau parameter valueslength(n) > 1, the length is
taken to be the number requiredGB1() returns a gamlss.family object which can be used to fit the GB1 distribution in the
gamlss() function.
dGB1() gives the density, pGB1() gives the distribution
function, qGB1() gives the quantile function, and rGB1()
generates random deviates.GB1), is defined as
$$f(y|\mu,\sigma\,\nu,\tau)= \frac{\tau \nu^\beta y^{\tau\alpha-1} (1-y^\tau)^{\beta-1}}{B(\alpha,\beta)[\nu+(1-\nu) y^\tau]^{\alpha+\beta}}$$where $0 < y < 1$, $\alpha = \mu(1-\sigma^2)/\sigma^2$ and $\beta=(1-\mu)(1-\sigma^2)/\sigma^2$, and $\alpha>0$, $\beta>0$. Note the $\mu=\alpha /(\alpha+\beta)$, $\sigma = (\alpha+\beta+1)^{-1/2}$. .
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
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,
gamlss.family, JSU, BCTGB1() #
y<- rGB1(200, mu=.1, sigma=.6, nu=1, tau=4)
hist(y)
# library(gamlss)
# histDist(y, family=GB1, n.cyc=60)
curve(dGB1(x, mu=.1 ,sigma=.6, nu=1, tau=4), 0.01, 0.99, main = "The GB1
density mu=0.1, sigma=.6, nu=1, tau=4")Run the code above in your browser using DataLab