The formation mechanisms of an inverse electron distribution function (EDF) in gas-discharge plasma are investigated. An approximate analytical model of an inverse EDF in an inhomogeneous electric field and the formation criteria are presented. It is shown that the regions of EDF inversion in classical glow discharges are located in the transition regions to the right and left of the positive column in areas with significant gradients of the electron density. An interesting feature of the EDF behavior in the vicinity of the second reversal point of the electric field is discovered in the numerical simulation results. At least one of the second-order partial derivatives in the solution of the Boltzmann kinetic equation for the isotropic part of the EDF has a discontinuity at this point.