Since coaches’ crashes have serious impacts on society, many attributes are studied as contributing factors related to the crashes. The present research work focuses on the existing statistical similarity between distribution functions of coaches’ crashes and their usage exposure in the Iranian intercity road network. Traffic volume is considered as an important usage exposure for intercity buses/coaches over the intercity road network, so this study aims to check whether coaches' traffic volume and the frequency of their crashes come from the same distribution functions. The two-sample distribution function test of Wilcoxon as well as the goodness of fit test called Kolmogorov-Smirnov have been utilized to check the statistical similarity between the distribution functions of coaches’ crashes and their usage exposure. Experimental data for coaches’ traffic volumes and their crashes have been collected for three years, and the above-mentioned methods have been performed using the proportion form of collected data due to the existing their different scales. After performing two methods of checking similarity, the results revealed there is no significant difference between the probability functions of traffic volumes, considered as usage exposure, and coaches’ crashes. It means that both attributes come from the same distribution functions. Traffic safety authorities and passenger transport operators who are dealing with traffic safety on the intercity public should be aware of the effects of traffic volumes on coaches' crashes on designing the routes and schedule for passenger transportation.