CS2e: The Cosine Sine Exponential family

In ousuga/RelDists: Estimation for some Reliability Distributions

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{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.

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

\insertRef

chesneau2018newRelDists

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"))

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.