The distribution function of pulmonary transit times (fPTTs) contains information on the transit time of blood through the lungs and the dispersion in transit times. Most of the previous studies have used specific functional forms with adjustable parameters to characterize the fPTT. It is the purpose here to investigate the possibility of estimating the fPTT in a model-free way. The method employs the maximum entropy principle and is used, in particular, on cardiac positron emission tomographic (PET) studies but is believed to be more generally applicable. Using this principle in a test case, we were able to accurately identify a two-peaked transfer function, which may theoretically be seen in patients with pulmonary disease confined to one lung. Transit time values for [13N]-ammonia were produced by applying the algorithm to PET studies from normal volunteers.