dUHLG: Unit Half Logistic-Geometry distribution

In ZeroOneDists: One Zero Statistical Distributions

Unit Half Logistic-Geometry distribution

Description

These functions define the density, distribution function, quantile function and random generation for the Unit Half Logistic-Geometry distribution with parameter \mu.

Usage

dUHLG(x, mu, log = FALSE)

pUHLG(q, mu, lower.tail = TRUE, log.p = FALSE)

qUHLG(p, mu, lower.tail = TRUE, log.p = FALSE)

rUHLG(n, mu)

Arguments

x, q	vector of (non-negative integer) quantiles.
mu	vector of the mu 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 Unit Half Logistic-Geometry distribution with parameter \mu has a support in (0, 1) and density given by

f(x| \mu) = \frac{2 \mu}{(\mu+(2-\mu)x)^2}

for 0 < x < 1 and \mu > 0.

Value

dUHLG gives the density, pUHLG gives the distribution function, qUHLG gives the quantile function, rUHLG generates random deviates.

Author(s)

Juan Diego Suarez Hernandez, [e-mail]

References

Ramadan, A. T., Tolba, A. H., & El-Desouky, B. S. (2022). A unit half-logistic geometric distribution and its application in insurance. Axioms, 11(12), 676.

See Also

UHLG.

Examples

# Example 1
# Plotting the density function for different parameter values
curve(dUHLG(x, mu=0.4), from=0.01, to=0.99,
      ylim=c(0, 5), lwd=2,
      col="black", las=1, ylab="f(x)")

curve(dUHLG(x, mu=1), lwd=2,
      add=TRUE, col="red")

curve(dUHLG(x, mu=2), lwd=2,
      add=TRUE, col="green")

curve(dUHLG(x, mu=7), lwd=2,
      add=TRUE, col="blue")

legend("topright",
       col=c("black", "red", "green", "blue"),
       lty=1, bty="n", lwd=2,
       legend=c("mu=0.4",
                "mu=1",
                "mu=2",
                "mu=7"))

# Example 2
# Checking if the cumulative curves converge to 1
curve(pUHLG(x, mu=0.25), lwd=2,
      from=0.001, to=0.999, col="black", las=1, ylab="F(x)")

curve(pUHLG(x, mu=0.7), lwd=2,
      add=TRUE, col="red")

curve(pUHLG(x, mu=1.8), lwd=2,
      add=TRUE, col="green")

curve(pUHLG(x, mu=2.2), lwd=2,
      add=TRUE, col="blue")

legend("bottomright", col=c("black", "red", "green", "blue"),
       lty=1, bty="n", lwd=2,
       legend=c("mu=0.25",
                "mu=0.7",
                "mu=1.8",
                "mu=2.2"))

# Example 3
# Checking the quantile function
mu <- 2
p <- seq(from=0.01, to=0.99, length.out=100)
plot(x=qUHLG(p, mu=mu), y=p,
     xlab="Quantile", las=1, ylab="Probability")
curve(pUHLG(x, mu=mu), add=TRUE, col="red")

# Example 4
# Comparing the random generator output with
# the theoretical density
x <- rUHLG(n=10000, mu=0.5)
hist(x, freq=FALSE)
curve(dUHLG(x, mu=0.5), lwd=2,
      col="tomato", add=TRUE, from=0.01, to=0.99)

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