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{π σ μ \exp(\frac{-x} {ν})}{2 ν [(μ\sin(\frac{π}{2} \exp(\frac{-x} {ν})) + σ\cos(\frac{π}{2} \exp(\frac{-x} {ν}))]^2},
for x > 0, μ > 0, σ > 0 and ν > 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
chesneau2018newRelDists
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
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