On v0.25.113 of Distributions.

PGeneralizedGaussian uses the default implementation of logccdf, which is just log(ccdf), so it can easily underflow.
Since the distribution is symmetrical, these two should be equal:

julia> logcdf(PGeneralizedGaussian(2.5), -5.0)
-59.8161755398042

julia> logccdf(PGeneralizedGaussian(2.5), 5.0)
-Inf

There's an easy workaround by rewriting in terms of logcdf, but it took a while to figure out where the Infs were coming from when this was buried in a more complex computation.

julia> _logccdf(d::PGeneralizedGaussian, x) = logcdf(d, 2*d.μ - x)
_logccdf (generic function with 1 method)

julia> _logccdf(PGeneralizedGaussian(2.5), 5.0)
-59.8161755398042