CS2e {RelDists}

The Cosine Sine Exponential family

Description

The Cosine Sine Exponential family

Usage

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.

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

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

Author(s)

Johan David Marin Benjumea, [e-mail]

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.

See Also

dCS2e

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"))