CS2e function

The Cosine Sine Exponential family

CS2e(mu.link = "log", sigma.link = "log", nu.link = "log")

Arguments

• mu.link: defines the mu.link, with "log" link as the default for the mu parameter.
• sigma.link: defines the sigma.link, with "log" link as the default for the sigma.
• nu.link: defines the nu.link, with "log" link as the default for the nu parameter.

Returns

Returns a gamlss.family object which can be used to fit a CS2e distribution in the gamlss() 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

# Example 1
# Generating some random values with
# known mu, sigma and nu 
y <- rCS2e(n=100, mu = 0.1, sigma =1, nu=0.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='CS2e',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
exp(coef(mod, what='mu'))
exp(coef(mod, what='sigma'))
exp(coef(mod, what='nu'))

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.45, max=0.55)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(0.2 - x1)
sigma <- exp(0.8 - x2)
nu <- 0.5
x <- rCS2e(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1,family=CS2e,
              control=gamlss.control(n.cyc=50000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")
exp(coef(mod, what="nu"))

References

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

See Also

dCS2e

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co