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.Comment: v1: 19 pages, LaTeX, no figures; v2: typos corrected and one reference removed to match published version in Phys. Rev.

In this work we construct a family of spherically symmetric, static, charged regular black hole metrics in the context of Einstein-nonlinear electrodynamics theory. The construction of the charged regular black hole metrics is based on three requirements: (a) the weak energy condition should be satisfied, (b) the energy-momentum tensor should have the symmetry $T^{0}_{0}=T^{1}_{1}$, and (c) these metrics have to asymptotically behave as the Reissner-Nordstr\"{o}m black hole metric. In addition, these charged regular black hole metrics depend on two parameters which for specific values yield regular black hole metrics that already exist in the literature. Furthermore, by relaxing the third requirement, we construct more general regular black hole metrics which do not behave asymptotically as a Reissner-Nordstr\"{o}m black hole metric.Comment: v1: 11 pages, LaTeX, no figures; v2: typos corrected and one reference removed to match published version in Phys. Lett.