BER2: Beta Rectangular distribution version 2

In ZeroOneDists: One Zero Statistical Distributions

Beta Rectangular distribution version 2

Description

The Beta Rectangular family

Usage

BER2(mu.link = "logit", sigma.link = "log", nu.link = "logit")

Arguments

mu.link	defines the mu.link, with "logit" link as the default for the mu parameter.
sigma.link	defines the sigma.link, with "log" link as the default for the sigma parameter.
nu.link	defines the nu.link, with "logit" link as the default for the nu parameter.

Details

The Beta Rectangular distribution with parameters mu, sigma and nu has density given by

f(x| \mu, \sigma, \nu) = \nu + (1 - \nu) b(x| \mu, \sigma)

for 0 < x < 1, 0 < \mu < 1, \sigma > 0 and 0 < \nu < 1. The function b(.) corresponds to the traditional beta distribution that can be computed by dbeta(x, shape1=mu*sigma, shape2=(1-mu)*sigma).

Value

Returns a gamlss.family object which can be used to fit a BER2 distribution in the gamlss() function.

References

Bayes, C. L., Bazán, J. L., & García, C. (2012). A new robust regression model for proportions. Bayesian Analysis, 7(4), 841-866.

See Also

dBER2

Examples

# Example 1
# Generating some random values with
# known mu and sigma
y <- rBER2(n=500, mu=0.3, sigma=7, nu=0.4)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, family=BER2,
               control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))

inv_logit(coef(mod1, what="mu"))
exp(coef(mod1, what="sigma"))
inv_logit(coef(mod1, what="nu"))

# Example 2
# Generating random values under some model

# A function to simulate a data set with Y ~ BER2
gendat <- function(n) {
  x1 <- runif(n, min=0.4, max=0.6)
  x2 <- runif(n, min=0.4, max=0.6)
  x3 <- runif(n, min=0.4, max=0.6)
  mu    <- inv_logit(-0.5 + 1*x1)
  sigma <- exp(-1 + 4.8*x2)
  nu    <- inv_logit(-1 + 0.5*x3)
  y <- rBER2(n=n, mu=mu, sigma=sigma, nu=nu)
  data.frame(y=y, x1=x1, x2=x2, x3=x3)
}

set.seed(1234)
datos <- gendat(n=500)

mod2 <- gamlss(y~x1, sigma.fo=~x2, nu.fo=~x3,
               family=BER2, data=datos,
               control=gamlss.control(n.cyc=500, trace=TRUE))

summary(mod2)

ZeroOneDists documentation built on March 7, 2026, 1:07 a.m.