LIF neuron model is a threshold-based neuron model and has been widely used to analytically study neuronal behavior as the easiness of the model. DDF provides a mechanism for including the previous values of the membrane potential on its further evolution and increases the model complexity. LIF neuron model in DDF is more closure to the real neuron as compared with the simple LIF neuron with noisy input. The spiking activity and neuronal information processing LIF neuron model with refractory time period has been investigated in DDF. In order to extend the study, three different kinds of the kernel function, namely, exponentially distributed, gamma-distributed and hypo-exponential distributed delay kernel function and two different kinds of refractory time period, namely, uniformly distributed and Gaussian distributed time periods are investigated. The obtained results are compared with no refractory time period results. We notice that the Gaussian distributed refractory time period with hypo-exponentially distributed delay kernel function has ISI distribution patterns more closure to the experimental studies.