Road Safety When Drivers Use Alcohol and Marijuana: Confounded Poisson Distribution Helps to Understand

Self-admitted users of alcohol and/or marijuana while driving haunt road safety regulating agencies in general and community groups such as Mothers Against Drunk Driving (MADD) in particular. Motivated by such data in a survey, by 6,612 drivers above 18 years old in USA during years 2013-2015, we thought of interpreting how the road safety is in the scenarios. Needless to emphasize the importance of any breach of road safety to nursing professionals working in emergency unit of a hospital as the victims of road accidents arrive there to get a preemptive service with urgency. To be educated on the issues, this article develops and uses an appropriate probability model, which is named Confounded Poisson Distribution (CPD). Statistical properties of CPD are derived and applied to analyze the data and to demystify the patterns in road safety among impaired drivers in the age brackets 18 through 75+ years.