I don't have a stats background let alone one in extreme value theory, and I have what I imagine is a simple question but one I that haven't been able to find the answer to. The cumulative distribution function for a GEV distribution is:
where $\xi, \mu$ and $\sigma$ represents a shape, location, and scale, respectively.
For this equation to work, $1 + \xi(x-\mu)/\sigma$ must be greater than zero.
My question is, what does one do when $1 + \xi(x-\mu)/\sigma$ is less than or equal to zero?
Given the GEV is a unification of the Gumbel, Fréchet and Weibull distributions, can I simply use the CDF for one of these distributions when the correct criteria apply. For example, if my shape parameter is negative (which seems to be the source of my issue) could I use the CDF for the Weibull distribution (e.g. see wikipedia)?
I'm repeating this process many times. I'm using R and the fevd function to fit my parameters, so I'm also not sure if my parameters are compatible with the three sub-families. I know there are functions to calculate the CDF but I'd like to do this manually.