Parametrizations in R and WinBUGS

Gamma distribution

WinBUGS
dgamma(a,b): Gamma distribution with parameter a and b.
  f(x)= b^a/( Gamma(a)) x^(a-1) e^-(b*x)
  mean=a/b
  variance=a/b^2
R
dgamma(x,shape=a,scale=s): Gamma distribution with parameter a and s.
  f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)
  mean=a*s
  variance=a*s^2

Weibull distribution

WinBUGS
dweib(nu, lambda): Weibull distribution with parameters nu and lambda.
  f(x)= nu * lambda * x^{nu-1} exp(-lambda * x^nu)
R
dweibull(x,shape=m,scale=eta): Weibull distribution with parameters m and eta.
  f(x) = (m/eta) * (x/eta)^{m-1} * exp(-(x/eta)^m)

Sample Codes

m and eta
model{
  for ( i in 1:n ) {
    t[i] ~ dweib(nu, lambda)I(tcen[i],)
  }
  nu ~ dgamma(10,0.1)
  ieta ~ dgamma(100,0.1)
  eta <- 1/ieta
  lambda <- 1/pow(eta, m)
  m <- nu
}

list(n=3,
t=c(NA,NA,NA),
tcen=c(97,97,97))

list(nu=1,ieta=0.1)
nu and lambda
model{
  for ( i in 1:n ) {
    t[i] ~ dweib(nu, lambda)I(tcen[i],)
  }
  nu ~ dgamma(100,0.1)
  lambda ~ dgamma(100,0.1)
  m <- nu
  eta <- pow(lambda,-1/nu)
}

list(n=3,
t=c(NA,NA,NA),
tcen=c(97,97,97))

list(nu=5,lambda=10)
bugs/how_to/weibull_distribution.txt · 最終更新: 2012/03/29 18:12 by watalu
 
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