LIN: The Lindley family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Lindley family

Description

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

mu.link

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

Details

The Lindley with parameter mu has density given by

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

for x > 0 and μ > 0.

Value

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

Author(s)

Freddy Hernandez [e-mail]

References

\insertRef

lindley1958fiducialRelDists

\insertRef

lindley1965introductionRelDists

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")

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

# 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)

coef(mod, what='mu')

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