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The Lindley family

Source: R/LIN.R
LIN.Rd

The function LIN() defines the Lindley distribution with only one parameter for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

LIN(mu.link = "log")

Arguments

defines the mu.link, with "log" link as the default for the mu parameter.

Value

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

Details

The Lindley with parameter mu has density given by

\(f(x) = \frac{\mu^2}{\mu+1} (1+x) \exp(-\mu x),\)

for x > 0 and \(\mu > 0\).

References

lindley1958fiducialRelDists

lindley1965introductionRelDists

Author

Freddy Hernandez fhernanb@unal.edu.co

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rLIN(n=200, mu=2)

# Fitting the model
require(gamlss)
mod <- gamlss(y ~ 1, family="LIN")
#> GAMLSS-RS iteration 1: Global Deviance = 228.0726 

# Extracting the fitted values for mu
# using the inverse link function
exp(coef(mod, what='mu'))
#> (Intercept) 
#>    2.051356 

# Example 2
# Generating random values under some model
n <- 100
x1 <- runif(n=n)
x2 <- runif(n=n)
eta <- 1 + 3 * x1 - 2 * x2
mu <- exp(eta)
y <- rLIN(n=n, mu=mu)

mod <- gamlss(y ~ x1 + x2, family=LIN)
#> GAMLSS-RS iteration 1: Global Deviance = -113.9316 
#> GAMLSS-RS iteration 2: Global Deviance = -113.9316 

coef(mod, what='mu')
#> (Intercept)          x1          x2 
#>    1.564129    2.477203   -2.225867