Interbreath interval (IBI), the time interval between breaths, and its variations in time around the mean, the IBI variability, are important measures associated with irregularity of breathing. The IBI histogram generally follows a power law distribution with its characterizing parameters changing with maturation. To assess the dynamics of breathing we propose a point process model of IBI with a lognormal parametric structure to appropriately represent the stochastic nature of the IBI distribution. We estimate the time varying evolution of the characterizing parameters to represent the dynamic nature of breathing, and thereby provide a time-varying measure of irregularity in breathing. The reliability of the model to capture the data is assessed using Kolmogorov-Smirnov (KS) and independence tests. Our results validate the novel approach in the assessment of the irregularity of breathing by analyzing respiratory recordings from newborn rats and preterm infants.