Specifying a Normal - Log-Normal Mixture (Skew Normall)

  • Nathan Lally
    Nathan Lally

    Hello and thank you in advance for your help.

    I am an actuary working on a Bayesian loss reserve model using incremental average severity data. Exploratory analysis of the response seems to suggest a skew normal distribution of some sort would be appropriate as there are some negative values in the left tail and the log transformed positive values fit a normal distribution fairly well. I was inspired by this posting http://www.casact.org/newsletter/index.cfm?fa=viewart&id=6544 by Glenn Meyers and feel like the latter parameterization should be easy to implement in JAGS. However, since I am not used to JAGS I am struggling to set the model up. Here is a example of what I am trying to do.

    #Likelihood (training set)
    for (i in 1:n){
      y[i] ~ dnorm(z[i], tau)
      z[i] ~ dlnorm(mu[i], tauln)
      mu[i] <- beta1*Dev[i] + ... 

    I am not sure how to handle the negative mu[i]s in the absence of control structures (if, else, etc...) I am used to. I need to pass the zero valued or negative mu[i]s directly to the mean parameter for my response y[i].

    Is there a clever way to do this with the step function? Should I consider specifying the normal - log-normal mixture another way?

    I appreciate your thoughts.

    FYI - I also posted this question here http://stats.stackexchange.com/questions/104079/specifying-a-normal-log-normal-mixture-skew-normall-in-winbugs-jags

    Last edit: Nathan Lally 2014-06-20