dBER2: Beta Rectangular distribution version 2

In ZeroOneDists: One Zero Statistical Distributions

Beta Rectangular distribution version 2

Description

These functions define the density, distribution function, quantile function and random generation for the Beta Rectangular distribution with parameters \mu, \sigma and \nu reparameterized to ensure E(X)=\mu.

Usage

dBER2(x, mu, sigma, nu, log = FALSE)

pBER2(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qBER2(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rBER2(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

dBER2 gives the density, pBER2 gives the distribution function, qBER2 gives the quantile function, rBER2 generates random deviates.

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

BER2.

Examples

# Example 1
# Plotting the density function for different parameter values
curve(dBER2(x, mu=0.5, sigma=10, nu=0),
      from=0, to=1, col="green", las=1, ylab="f(x)")

curve(dBER2(x, mu=0.5, sigma=10, nu=0.2),
      add=TRUE, col= "blue1")

curve(dBER2(x, mu=0.5, sigma=10, nu=0.4),
      add=TRUE, col="yellow")

curve(dBER2(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(dBER2(x, mu=0.3, sigma=10, nu=0),
       from=0, to=1, col="green", las=1, ylab="f(x)")

curve(dBER2(x, mu=0.3, sigma=10, nu=0.2),
       add=TRUE, col= "blue1")

curve(dBER2(x, mu=0.3, sigma=10, nu=0.4),
       add=TRUE, col="yellow")

curve(dBER2(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=0.3, sigma=10, nu=0",
                "mu=0.3, sigma=10, nu=0.2",
                "mu=0.3, sigma=10, nu=0.4",
                "mu=0.3, sigma=10, nu=0.6"))


# Example 2
# Checking if the cumulative curves converge to 1
curve(pBER2(x, mu=0.5, sigma=10, nu=0),
       from=0, to=1, col="green", las=1, ylab="f(x)")

curve(pBER2(x, mu=0.5, sigma=10, nu=0.2),
       add=TRUE, col= "blue1")

curve(pBER2(x, mu=0.5, sigma=10, nu=0.4),
       add=TRUE, col="yellow")

curve(pBER2(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=qBER2(p, mu=mu, sigma=sigma, nu=nu), y=p,
     xlab="Quantile", las=1, ylab="Probability")
curve(pBER2(x, mu=mu, sigma=sigma, nu=nu), add=TRUE, col="red")

# Example 4
# Comparing the random generator output with
# the theoretical density
x <- rBER2(n= 10000, mu=0.3, sigma=10, nu=0.1)
hist(x, freq=FALSE)
curve(dBER2(x, mu=0.3, sigma=10, nu=0.1),
      col="tomato", add=TRUE)

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