RelDists (version 1.0.1)

WALD: The Wald family

Description

The function WALD() defines the wALD distribution, two-parameter continuous distribution for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

WALD(mu.link = "log", sigma.link = "log")

Value

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

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 parameter.

Author

Sofia Cuartas García,

Details

The Wald distribution with parameters \(\mu\) and \(sigma\) has density given by

\(\operatorname{f}(x |\mu, \sigma)=\frac{\sigma}{\sqrt{2 \pi x^3}} \exp \left[-\frac{(\sigma-\mu x)^2}{2x}\right ], x>0 \)

References

Heathcote, A. (2004). Fitting Wald and ex-Wald distributions to response time data: An example using functions for the S-PLUS package. Behavior Research Methods, Instruments, & Computers, 36, 678-694.

See Also

dWALD.

Examples

# Example 1
# Generating random values with
# known mu and sigma
require(gamlss)
mu <- 1.5
sigma <- 4.0

y <- rWALD(10000, mu, sigma)

mod1 <- gamlss(y~1, sigma.fo=~1,  family="WALD",
               control=gamlss.control(n.cyc=5000, trace=TRUE))

exp(coef(mod1, what="mu"))
exp(coef(mod1, what="sigma"))

# Example 2
# Generating random values under some model

# A function to simulate a data set with Y ~ WALD
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu <- exp(0.75 - 0.69 * x1)   # Approx 1.5
  sigma <- exp(0.5 - 0.64 * x2) # Approx 1.20
  y <- rWALD(n, mu, sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

dat <- gendat(n=200)

mod2 <- gamlss(y~x1, sigma.fo=~x2, family=WALD, data=dat, 
               control=gamlss.control(n.cyc=5000, trace=TRUE))

summary(mod2)