A new line intensity distribution function is introduced in order to improve the accuracy of statistical narrow-band (SNB) models in the Doppler line broadening regime and in a wide temperature range. This distribution function generalizes the Malkmus distribution through a parameter enabling to adjust the contribution of small line intensities. This new model is shown to enhance significantly SNB accuracy for CO2 uniform column radiation, especially at low temperatures. For non-uniform columns, Lindquist–Simmons type approximations are derived for this new intensity distribution. Their results are in much closer agreement with line by line results than Curtis–Godson approximation ones when steep temperature gradients are considered.