As the Internet of Things (IoT) technology is being deployed, the demand for radio spectrum is increasing. Cognitive radio (CR) is one of the most promising solutions to allow opportunistic spectrum access for IoT secondary users through utilizing spectrum holes resulting from the underutilization of frequency spectrum. A CR needs to frequently sense the spectrum to avoid interference with primary users (PUs). Compressive spectrum sensing techniques have been gaining increasing interest in wideband spectrum sensing, as they reduce the need for high-rate analog-to-digital converters, reducing the complexity and energy requirements of the CR. In order to enhance spectrum sensing performance, researchers proposed to incorporate PU spectrum usage information into the process of spectrum sensing. Spectrum usage information can be obtained through pilot signals, geo-locational databases or through evaluation of previous spectrum sensing results. In this paper, we are studying the effects of compressive sensing parameters namely compression ratio, sensing period, and sensing duration on the estimation of primary user behavior statistics. We achieved an accurate estimation of the primary user's behavior while saving 40% of the sampling rate by using compressive spectrum sensing compared to traditional spectrum sensing with Nyquist rate sampling.