Cognitive Radio (CR) systems are a promising solution to the spectrum scarcity problem. However, accurate modeling of spectrum utilization is essential to obtain a better quantitative understanding of important concepts of CR systems. Compact mathematical formulations that describe the realistic spectrum usage would improve the recent theoretical work to a large extent. The data generated from such models would also increase the quality of the simulation based research in the aspect of realism. Besides, in practice, measurement campaigns would prefer if they could characterize results with a few well known parameters instead of exchanging large amount of data. Therefore, in this paper we try to come up with a mathematical model for the spectrum usage by estimating the Probability Mass Function (PMF) of the number of occupied channels. Note that this also gives an insight regarding the spectrum availability. To do this, the data collected from a spectrum occupancy measurement campaign conducted in the State of Qatar is used. The measurements are performed over three consecutive days considering 700-3000 MHz frequency band at four different locations concurrently. We show that after applying the Chi square test, the Log-Normal distribution fits the best among other candidates to the empirical PMF independent of location and the threshold used to define a channel as occupied.