A new class of zero-truncated counting models and its application

Count data is a type of data derived from the number of times an event occurs per unit of time, and zero-truncated count data refers to count data without zero, which often appears in various fields. In this paper, a new zero-truncated Bell (ZTBell) distribution is proposed on the basis of Bell distribution. We studied its statistical properties, exploring methods such as maximum likelihood estimation (MLE), expectation-maximization (EM) algorithm, and minimization-maximization (MM) algorithm for parameter estimation, as well as conducting likelihood ratio tests. In addition, we used the Bootstrap method to calculate the standard errors and confidence intervals of the parameters. The simulation results found that all of the MLE, MM algorithm and EM algorithm are effective. And, as the sample size increases, the estimates of the parameters are closer to the true values and the root mean square error is smaller. Finally, applying the model to a set of factory accident data, we found that the ZTBell distribution fits better than the other models and is close to the fitting results of the zero-truncated generalized Poisson distribution. But ZTBell distribution has only one parameter, so it's even simpler compared to the latter. Therefore, the ZTBell distribution can be a good alternative to other zero-truncated distributions, which provides more options available for statistical analysis in this domain.