examples/examples_dCJ2.R

In ousuga/RelDists: Estimation for some Reliability Distributions

# 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)