Evaluation of parameter estimation methods for a new zero-truncated Poisson moment exponential distribution with real-life application

The zero-truncated distribution for count data has recently received considerable attention in many fields, especially in real-life applications in which only positive counts are observed. This paper proposes a new zero-truncated model based on the Poisson-moment exponential distribution. The important statistical properties of the distribution are studied in terms of the moment generating function, expected value, variance, and dispersion index. For statistical inference, the new estimator and confidence interval for the parameter of the zero-truncated Poisson moment exponential distribution are introduced. These are based on parametric and non-parametric estimation. The effectiveness of the methods is evaluated using simulations. The results show that the maximum likelihood estimator has good bias behaviour and consistency. The modified standard bootstrap confidence interval introduced in this paper performs well in terms of coverage probability and expected length for all sample sizes and all levels of the parameter. The approaches are illustrated by analyzing two real-data applications on the infant mortality rate and earthquake counts.