Artificial intelligence (AI) has been become the primary need in nearly all sectors namely engineering, services, banking, finance, defense, space etc [3], [33]. Artificial intelligence in these sectors can be implemented in two ways: (i) hardware level implementation (ii) software level implementation. Both kinds of AI implementation require neuron models which mimic the minimal set of real neuron functionality. To this end, Leaky Integrate-and-Fire (LIF) model is performing as the backbone for both kinds of AI implementation. At hardware level implementation, it’s a variant, called as neuristors, is used at chip level implementation, whereas a number of variants LIF model are used to implement AI at software level. In this work, the extended LIF model in distributed delay kernel regime is analyzed. The impact of exponentially distributed delay (EDD) memory kernel on spiking activity and steady state membrane potential distribution (SVD) of LIF neuron is investigated. Fokker-Planck equation associated with the considered model is solved to investigate SVD of the neuron in sub-threshold regime, which results Gaussian distribution. In order to study the information processing, spiking activity of the model is investigated, which is further extended to neuronal rate-code scheme. These finding have been compared with simple LIF model with stochastic input. It is evident that steady state membrane potential distribution of the LIF neuron is invariant due to the presence of EDD. Such kinds of neuron models are useful to implement artificial neural networks. To this end, the proposed model can used to implement recurrent neural networks (RNN) with comparatively more accuracy. Similarly, this model can also be investigated in term of chip level implementation of AI.