  We construct several charged regular black hole metrics employing mass
distribution functions which are inspired by continuous probability
distributions. Some of these metrics satisfy the weak energy condition and
asymptotically behave as the Reissner--Nordstrom black hole. In each case, the
source to the Einstein equations corresponds to a nonlinear electrodynamics
model, which in the weak field limit becomes the Maxwell theory (compatible
with the Maxwell weak field limit or approximation). Furthermore, we include
other regular black hole solutions that satisfy the weak energy condition and
some of them correspond to the Maxwell theory in the weak field limit.
