dCS2e {RelDists}

The Cosine Sine Exponential distribution

Description

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

Usage

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.

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.

Value

dCS2e gives the density, pCS2e gives the distribution function, qCS2e gives the quantile function, rCS2e generates random deviates and hCS2e gives the hazard function.

Author(s)

Juan Pablo Ramirez

References

Chesneau C, Bakouch HS, Hussain T (2018). “A new class of probability distributions via cosine and sine functions with applications.” Communications in Statistics-Simulation and Computation, 1–14.

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