The optical permittivity of monocrystalline direct bandgap semiconductors can be described well by critical point models based on parabolic band approximation (CPPB). However, the optical permittivity of polycrystalline direct bandgap semiconductors like halide perovskite thin films requires a more precise description. Till now, only thermal bandgap fluctuation or exponential decay of density of states is incorporated into the CPPB model. We present an analytical calculation that is based on the CPPB model with only one additional physical assumption, namely, the Gaussian distributed bandgap energies (GCPPB). Furthermore, the GCPPB model satisfies the Kramers-Kronig causality relation.