log hazard function in R

Question

I'm trying to write out the log hazard function of the lognormal distribution and use this in R.

Using the survival function:

and the hazard function:

I have the following for the log(hazard):

log(hazard) = $-\log(2\pi)/2-\log(\sigma)-\log(t) - ((\log(t)-\mu)^2)/(2\sigma^2) - \log(1-\phi((\log(t)-\mu)/\sigma))$

In R I think this should be:

log(hazard) = -0.5*log(2*pi)-log(sigma)-log(t) - 
               ((log(t)-mu)^2)/(2*sigma^2) - 
               log(1-pnorm(log(t),mu,sigma))

Can anyone confirm whether this is the correct syntax to use?

Thanks in advance.

Answer 1

I think that's right. But I'm not going into to really check the details because it's unnecessary. It's much easier to calculate the log hazard directly from the definition. In other words,

logNormLogHaz <- function(x, mu, s){
    dens_vals <- dnorm(x, mu, s)
    s_vals <- 1 - pnorm(x, mu, s)
    logHazs <- log(dens_vals) - log(s_vals)
    ## More numerically stable then
    ## logHazs <- log(dens_vals/s_vals) *I think*
    return(logHazs)
}

And if you have a very good reason for explicitly writing it out as you have, you can at least use the above function to check that your new function is correct.