The data set is from crime sociology consisting of a sample of 4301 people with deviating behavior.
Recently, it was used by Zhang et al. (2016) and fitted by the zero-and-one inflated Poisson distribution.
References
Zhang, C., Tian, G. L., & Ng, K. W. (2016). Properties of the zero-and-one inflated Poisson distribution and likelihood-based inference methods. Statistics and its Interface, 9(1), 11-32.