param.startOW function

Initial values extraction for Odd Weibull distribution

This function can be used to extract initial values found with empirical time on test transform (TTT) through initValuesOW function. This is used for parameter estimation in OW distribution.

param.startOW(param, initValOW)

Arguments

• param: a character used to specify the parameter required. It can take the values "sigma" or "nu".

• initValOW: an initValOW object generated with initValuesOW

  function.

Returns

A length-one vector numeric value corresponding to the initial value of the parameter specified in param extracted from a initValuesOW

object specified in the initValOW input argument.

Details

This function just gets initial values computed with initValuesOW

for OW family. It must be called in sigma.start and nu.start

arguments from gamlss function. This function is useful only if user want to set start values automatically with TTT plot. See example for an illustration.

Examples

# Random data generation (OW distributed)
y <- rOW(n=500, mu=0.05, sigma=0.6, nu=2)

# Initial values with TTT plot
iv <- initValuesOW(formula = y ~ 1)
summary(iv)

# This data is from unimodal hazard
# See TTT estimate from sample
plot(iv, legend_options=list(pos=1.03))

# See the true hazard
curve(hOW(x, mu=0.05, sigma=0.6, nu=2), to=100, lwd=3, ylab="h(x)")

# Finally, we fit the model
require(gamlss)
con.out <- gamlss.control(n.cyc = 300, trace = FALSE)
con.in <- glim.control(cyc = 300)

(sigma.start <- param.startOW("sigma", iv))
(nu.start <- param.startOW("nu", iv))

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, control=con.out, i.control=con.in,
              family=myOW_region(OW(sigma.link="identity", nu.link="identity"),
                                 valid.values="auto", iv),
              sigma.start=sigma.start, nu.start=nu.start)

# Estimates are close to actual values
(mu <- exp(coef(mod, what = "mu")))
(sigma <- coef(mod, what = "sigma"))
(nu <- coef(mod, what = "nu"))

Author(s)

Jaime Mosquera Gutiérrez jmosquerag@unal.edu.co