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.

Value

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 \(\nu > 0\).

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.

Author

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

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'))
#> (Intercept) 
#>   0.1354098 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>   0.9996795 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>   0.4154714 

# 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")
#> (Intercept)          x1 
#>    3.691906   -9.078192 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>  -0.4190567   0.8326658 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>   0.5941255