dCS2e function

The Cosine Sine Exponential distribution

Density, distribution function, quantile function, random generation and hazard function for the Cosine Sine Exponential distribution with parameters mu, sigma and nu.

dCS2e(x, mu, sigma, nu, log = FALSE)

pCS2e(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qCS2e(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rCS2e(n, mu, sigma, nu)

hCS2e(x, mu, sigma, nu)

Arguments

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

Returns

dCS2e gives the density, pCS2e gives the distribution function, qCS2e gives the quantile function, rCS2e

generates random deviates and hCS2e gives the hazard function.

Details

The Cosine Sine Exponential Distribution with parameters mu, sigma and nu has density given by

$f(x)=\frac{\pi \sigma \mu \exp(\frac{-x} {\nu})}{2 \nu [(\mu\sin(\frac{\pi}{2} \exp(\frac{-x} {\nu})) + \sigma\cos(\frac{\pi}{2} \exp(\frac{-x} {\nu}))]^2},$

for $x > 0$, $\mu > 0$, $\sigma > 0$ and $\nu > 0$.

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
par(mfrow=c(1,1))
curve(dCS2e(x, mu=1, sigma=0.1, nu =0.1), from=0, to=1,
      ylim=c(0, 3), col="red", las=1, ylab="f(x)")
      
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pCS2e(x, mu=1, sigma=0.1, nu =0.1),
      from=0, to=1,  col="red", las=1, ylab="F(x)")
curve(pCS2e(x, mu=1, sigma=0.1, nu =0.1, lower.tail=FALSE),
      from=0, to=1, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qCS2e(p, mu=0.1, sigma=1, nu=0.1), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pCS2e(x, mu=0.1, sigma=1, nu=0.1), from=0, add=TRUE, col="red")

## The random function
hist(rCS2e(n=10000, mu=0.1, sigma=1, nu=0.1), freq=FALSE,
     xlab="x", las=1, main="")
curve(dCS2e(x, mu=0.1, sigma=1, nu=0.1), from=0, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hCS2e(x, mu=1, sigma=0.1, nu =0.1), from=0, to=1, ylim=c(0, 10),
      col=2, ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

References

Rdpack::insert_ref(key="chesneau2018new",package="RelDists")

Author(s)

Juan Pablo Ramirez