The inversion of the electron energy distribution function (EEDF) at low energies and the absolute negative electron conductivity are predicted and confirmed by numerical modeling of a direct current glow discharge in argon. It is shown that, in contrast to the local approximation used earlier for searching the inverse EEDF, in a real gas-discharge plasma, the formation of the EEDF is significantly affected by the terms with spatial gradients in the Boltzmann kinetic equation. In analogy with the inverse population of excited states in lasers, such a medium will amplify electromagnetic waves.