Inflated models are used whenever there are too many frequencies at a given count. In this regard, Poisson moment exponential distribution and a distribution to a point mass at zero are used to create a zeroinflated model namely Zero-Inflated Poisson Moment Exponential Distribution. Its distributional and reliability characteristics are investigated in some detail. A simulation exercise is undertaken to evaluate the effectiveness of the maximum likelihood estimators. The adaptability of the suggested distribution is demonstrated using three real datasets from various domains (e.g., vaccine adverse events, medical science data, epileptic seizure counts). The suggested distribution and the Poisson moment exponential distribution are distinguished by using the two different test procedures.