WALD: The Wald family

In ousuga/RelDists: Estimation for some Reliability Distributions

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")

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.

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

Value

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

Author(s)

Sofia Cuartas García, [e-mail]

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)

ousuga/RelDists documentation built on July 4, 2025, 10:55 a.m.