dCJ2: The two-parameter Chris-Jerry distribution

In RelDists: Estimation for some Reliability Distributions

The two-parameter Chris-Jerry distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the two-parameter Chris-Jerry distribution with parameters mu and sigma.

Usage

dCJ2(x, mu, sigma, log = FALSE)

pCJ2(q, mu, sigma, log.p = FALSE, lower.tail = TRUE)

qCJ2(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)

rCJ2(n, mu, sigma)

hCJ2(x, mu, sigma, log = FALSE)

Arguments

x, q	vector of quantiles.
mu	parameter.
sigma	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 observations.

Details

The two-parameter Chris-Jerry distribution with parameters mu and sigma has density given by

f(x; \sigma, \mu) = \frac{\mu^2}{\sigma \mu + 2} (\sigma + \mu x^2) e^{-\mu x}; \quad x > 0, \quad \mu > 0, \quad \sigma > 0

Note: In this implementation we changed the original parameters \theta for \mu and \lambda for \sigma, we did it to implement this distribution within gamlss framework.

Value

dCJ2 gives the density, pCJ2 gives the distribution function, qCJ2 gives the quantile function, rCJ2 generates random deviates and hCJ2 gives the hazard function.

Author(s)

Manuel Gutierrez Tangarife, [e-mail]

References

Chinedu, Eberechukwu Q., et al. "New lifetime distribution with applications to single acceptance sampling plan and scenarios of increasing hazard rates" Symmetry 15.10 (2023): 188.

See Also

CJ2

Examples

# Example 1
# Plotting the density function for different parameter values
curve(dCJ2(x, mu=3.5, sigma=0.01), 
      from=0.0001, to=5,
      ylim=c(0, 1),
      col="red", lwd=2,
      main="Density function",
      xlab="x", ylab="f(x)")
curve(dCJ2(x, mu=2, sigma=0.05),
      col="green",
      lwd=2,
      add=TRUE)
curve(dCJ2(x, mu=1.5, sigma=0.01),
      col="blue",
      lwd=2,
      add=TRUE)
curve(dCJ2(x, mu=2.5, sigma=0.01),
      col="lightblue",
      lwd=2,
      add=TRUE)
legend("topright", legend=c("mu=3.5, sigma=0.01",
                            "mu=2, sigma=0.05",
                            "mu=1.5, sigma=0.01",
                            "mu=2.5, sigma=0.1"),
       col=c( "red", "green","blue","lightblue"), lwd=2, cex=0.6)

# Example 2
# Checking if the cumulative curves converge to 1
curve(pCJ2(x, mu=2.7, sigma=0.1),
      from=0.0001, to=5,
      ylim=c(0, 1),
      col="red", lwd=2,
      main="Cumulative function",
      xlab="x", ylab="f(x)")
curve(pCJ2(x, mu=2.3, sigma=0.5),
      col="green",
      lwd=2,
      add=TRUE)
curve(pCJ2(x, mu=2.8, sigma=0.2),
      col="blue",
      lwd=2,
      add=TRUE)
curve(pCJ2(x, mu=3.8, sigma=0.3),
      col="lightblue",
      lwd=2,
      add=TRUE)
legend("bottomright", legend=c("mu=2.75, sigma=0.1",
                            "mu=2.3, sigma=0.5",
                            "mu=2.8, sigma=0.2",
                            "mu=3.8, sigma=0.3"),
       col=c( "red", "green","blue","lightblue"), lwd=2, cex=0.6)

# Example 3
# Checking the quantile function
p <- seq(from=0.0001, to=0.99999, length.out=100)
plot(x=qCJ2(p, mu=2.3, sigma=1.7), y=p, xlab="Quantile",
     las=1, ylab="Probability", main="Quantile function ")
curve(pCJ2(x, mu=2.3, sigma=1.7), 
      from=0.0001, add=TRUE, col="red", lwd=2.5)

# Example 4
# Comparing the random generator output with
# the theoretical probabilities
x <- rCJ2(n=10000, mu=1.5, sigma=2.5)
hist(x, freq=FALSE)
curve(dCJ2(x, mu=1.5, sigma=2.5), from=0.001, to=8, 
      add=TRUE, col="tomato", lwd=2)

# Example 5
# The Hazard function
curve(hCJ2(x, mu=0.85, sigma=0.15),
      from=0.0001, to=5,
      ylim=c(0, 1),
      col="red", lwd=2,
      main="Hazard function",
      xlab="x", ylab="f(x)")
curve(hCJ2(x, mu=1, sigma=0.05),
      col="green",
      lwd=2,
      add=TRUE)
curve(hCJ2(x, mu=0.9, sigma=0.1),
      col="blue",
      lwd=2,
      add=TRUE)
curve(hCJ2(x, mu=1.15, sigma=0.1),
      col="lightblue",
      lwd=2,
      add=TRUE)
legend("bottomright", legend=c("mu=0.85, sigma=0.15",
                               "mu=1, sigma=0.05",
                               "mu=0.9, sigma=0.1",
                               "mu=1.15, sigma=0.1"),
       col=c( "red", "green","blue","lightblue"), lwd=2, cex=0.5)

RelDists documentation built on Feb. 24, 2026, 5:09 p.m.