model{

for ( i in 1 : 2492){

dummy[i] <- 0
dummy[i] ~ dloglik(logLike[i])
logLike[i] <-

log(r/phi(alpha * sigma)) * ( 1 - stepxtheta[i] ) + log(1-r) * stepxtheta[i] +

( -0.5 * log(2 * pi) - log( x[i] ) - log( sigma ) - 0.5 * pow( (log(x[i])- mu)/ sigma, 2) ) *
( 1 - stepxtheta[i] ) +
( log(alpha) + alpha * log(theta) - (alpha+1)* log( x[i]) ) * stepxtheta[i]

stepxtheta[i] <- step( x[i] - theta )

}

theta ~ dgamma( 0.001, 0.001) # dexp( 0.5 ) #
alpha ~dgamma( 0.001, 0.001) # dexp( 0.5 ) #
sigma ~ dgamma(0.001, 0.001) # dexp( 0.5 ) #

r <- (sqrt(2*pi)*alpha*sigma*phi(alpha*sigma))
/(sqrt(2*pi)*alpha*sigma*phi(alpha*sigma)+exp(-0.5* pow(alpha* sigma,2)))
mu <- log(theta)- alpha*pow(sigma,2)
pi <-3.14159565


xf <- xa * delta + xb * ( 1 - delta )
xa ~ dlnorm( mu, tau ) I( , theta )
xb ~ dpar( alpha, theta )

delta ~ dbern( r )
tau <- 1/pow(sigma,2)


}