dCS2e | R Documentation |
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)
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. |
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
.
dCS2e
gives the density, pCS2e
gives the distribution
function, qCS2e
gives the quantile function, rCS2e
generates random deviates and hCS2e
gives the hazard function.
Juan Pablo Ramirez
Chesneau, C., Bakouch, H. S., & Hussain, T. (2019). A new class of probability distributions via cosine and sine functions with applications. Communications in Statistics-Simulation and Computation, 48(8), 2287-2300.
CS2e
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
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.