A New Alpha Power Transformation of Logistic Distribution With Its Properties and Applications

With the increasing complexity of datasets from various application areas, there is a growing demand for more flexible probability distributions for data modeling. This study introduces a novel probability distribution, the alpha power transformed logistic distribution, from the base logistic distribution using an alpha power transformation technique. Essential properties of the new probability distribution are derived and discussed. The new probability distribution is found to have more flexible hazard shapes with monotonically increasing and bumping behaviors. A simulation study using the acceptance‐rejection algorithm is carried out to generate random observations from the model and to investigate the performance of the new distribution. Parameter estimation is performed via the maximum likelihood estimation method. Two real data sets are used to demonstrate how well alpha power transformed logistic distribution fits to the data compared to base probability distribution and other competing probability distributions in an applied setting. Based on standard model selection criteria, we show that a new probability distribution performs better compared to its base distribution and other competing probability distributions. Numerical results and plots are performed using R software. The newly proposed probability distribution reveals interesting properties with the flexible shape of its hazard function and could be considered as a new contribution to the field of the statistical theory. Statistical inferences including fitting the model to data in some application areas, parameter estimation, and random sampling from the distribution can lead to new knowledge in the applied probability and statistics and application areas such as lifetime and reliability data. This finding can help as a groundwork for future studies in the field.