dBER: Beta Rectangular distribution

In ZeroOneDists: One Zero Statistical Distributions

Beta Rectangular distribution

Description

These functions define the density, distribution function, quantile function and random generation for the Beta Rectangular distribution with parameters \mu, \sigma and \nu.

Usage

dBER(x, mu, sigma, nu, log = FALSE)

pBER(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qBER(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rBER(n, mu, sigma, nu)

Arguments

x, q	vector of (non-negative integer) quantiles.
mu	vector of the mu parameter.
sigma	vector of the sigma parameter.
nu	vector of the nu parameter.
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 random values to return.

Details

The Beta Rectangular distribution with parameters \mu, \sigma and \nu has a support in (0, 1) and 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

dBER gives the density, pBER gives the distribution function, qBER gives the quantile function, rBER generates random deviates.

Author(s)

Karina Maria Garay, [e-mail]

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

BER.

Examples

# Example 1
# Plotting the density function for different parameter values
curve(dBER(x, mu=0.5, sigma=10, nu=0),
      from=0, to=1, col="green", las=1, ylab="f(x)")

curve(dBER(x, mu=0.5, sigma=10, nu=0.2),
      add=TRUE, col= "blue1")

curve(dBER(x, mu=0.5, sigma=10, nu=0.4),
      add=TRUE, col="yellow")

curve(dBER(x, mu=0.5, sigma=10, nu=0.6),
      add=TRUE, col="red")

legend("topleft", col=c("green", "blue1", "yellow", "red"),
       lty=1, bty="n",
       legend=c("mu=0.5, sigma=10, nu=0",
                "mu=0.5, sigma=10, nu=0.2",
                "mu=0.5, sigma=10, nu=0.4",
                "mu=0.5, sigma=10, nu=0.6"))


curve(dBER(x, mu=0.3, sigma=10, nu=0),
       from=0, to=1, col="green", las=1, ylab="f(x)")

curve(dBER(x, mu=0.3, sigma=10, nu=0.2),
       add=TRUE, col= "blue1")

curve(dBER(x, mu=0.3, sigma=10, nu=0.4),
       add=TRUE, col="yellow")

curve(dBER(x, mu=0.3, sigma=10, nu=0.6),
       add=TRUE, col="red")

legend("topright", col=c("green", "blue1", "yellow", "red"),
       lty=1, bty="n",
       legend=c("mu=0.5, sigma=10, nu=0",
                "mu=0.5, sigma=10, nu=0.2",
                "mu=0.5, sigma=10, nu=0.4",
                "mu=0.5, sigma=10, nu=0.6"))


# Example 2
# Checking if the cumulative curves converge to 1
curve(pBER(x, mu=0.5, sigma=10, nu=0),
       from=0, to=1, col="green", las=1, ylab="f(x)")

curve(pBER(x, mu=0.5, sigma=10, nu=0.2),
       add=TRUE, col= "blue1")

curve(pBER(x, mu=0.5, sigma=10, nu=0.4),
       add=TRUE, col="yellow")

curve(pBER(x, mu=0.5, sigma=10, nu=0.6),
       add=TRUE, col="red")

legend("topleft", col=c("green", "blue1", "yellow", "red"),
       lty=1, bty="n",
       legend=c("mu=0.5, sigma=10, nu=0",
                "mu=0.5, sigma=10, nu=0.2",
                "mu=0.5, sigma=10, nu=0.4",
                "mu=0.5, sigma=10, nu=0.6"))

# Example 3
# Checking the quantile function
mu <- 0.5
sigma <- 10
nu <- 0.4
p <- seq(from=0.01, to=0.99, length.out=100)
plot(x=qBER(p, mu=mu, sigma=sigma, nu=nu), y=p,
     xlab="Quantile", las=1, ylab="Probability")
curve(pBER(x, mu=mu, sigma=sigma, nu=nu), add=TRUE, col="red")

# Example 4
# Comparing the random generator output with
# the theoretical density
x <- rBER(n= 10000, mu=0.5, sigma=10, nu=0.1)
hist(x, freq=FALSE)
curve(dBER(x, mu=0.5, sigma=10, nu=0.1),
      col="tomato", add=TRUE)

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