© 2022, Thai Statistical Association. All rights reserved.This article proposes a new three parameter distribution in the family of the exponential distribution called the alpha power shifted exponential (APOSE) distribution. The structural mathematical properties of the APOSE model were derived and examined. The APOSE model parameters were established and obtained by maximum likelihood method. The flexibility, efficiency, and behavior of the APOSE model estimators were examined. The results show that the APOSE distribution is increasing, decreasing, unimodal, and right skewed property. The bivariate model of the APOSE distribution was also proposed. The empirical applicability and proficiency of the APOSE model was examined by a real-life dataset. The empirical results show that the proposed APOSE model provides a better goodness-of-fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.