Hypoxemia, characterized by low blood oxygen levels is pervasive in preterm infants and is associated with development of multiple adverse cardiovascular morbidities. In clinical practice, it is often quantified using frequency, pattern and time spent in it. A predictive tool of hypoxemia occurrence will aid clinicians in risk stratifying infant oxygenation patterns and improving personalized care. As a first step towards this goal in characterizing the underlying temporal processes, we studied inter-hypoxemia interval distributions in preterm infants on oxygen supplementation. We derived regression relationships of characterizing parameters of the distributions with gestational age and birth weight of infants. The modeling and goodness of fit tests of pooled and individual inter-hypoxemia intervals indicated that the inverse Gaussian and Birnbaum Saunders distributions fit well over short time scales and the lognormal at longer time scales. Information from distribution modeling may provide insights into hypoxemia recurrence times and be helpful in developing models to predict severe hypoxemic events that may be translated to personalized care in clinical settings. Clinical relevance - Understanding the stochastic nature of temporal processes underlying hypoxemia in preterm infants is a critical step towards developing predictive models for their occurrence. This may potentially aid in the neonatal care and treatment of these vulnerable infants.