PL | R Documentation |
Power Lindley distribution
PL(mu.link = "log", sigma.link = "log")
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. |
The Power Lindley Distribution with parameters mu
and sigma
has density given by
f(x) = \frac{μ σ^2}{σ + 1} (1 + x^μ) x ^ {μ - 1} \exp({-σ x ^μ}),
for x > 0.
Returns a gamlss.family object which can be used to fit a PL distribution in the gamlss()
function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefGhitanya2013RelDists
dPL
# Example 1 # Generating some random values with # known mu and sigma y <- rPL(n=100, mu=1.5, sigma=0.2) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, family= 'PL', control=gamlss.control(n.cyc=5000, trace=FALSE)) # Extracting the fitted values for mu and sigma # using the inverse link function exp(coef(mod, 'mu')) exp(coef(mod, 'sigma')) # Example 2 # Generating random values under some model n <- 200 x1 <- runif(n, min=0.4, max=0.6) x2 <- runif(n, min=0.4, max=0.6) mu <- exp(1.2 - 2 * x1) sigma <- exp(0.8 - 3 * x2) x <- rPL(n=n, mu, sigma) mod <- gamlss(x~x1, sigma.fo=~x2, family=PL, control=gamlss.control(n.cyc=5000, trace=FALSE)) coef(mod, what="mu") coef(mod, what="sigma")
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