Modeling Extreme Values with Alpha Power Inverse Pareto Distribution

• Main Authors: Atta, H. (Author), Badshah, S. (Author), Ihtisham, S. (Author), Ijaz, M. (Author), Khalil, A. (Author), Manzoor, S. (Author)
• Format: Article
• Language: English
• Published: Sciendo 2023
• Subjects: Entropy; Extreme value; Extreme Values; Inverse pareto distribution; Inverse Pareto distribution; Inverse problems; Maximum likelihood estimation; Pareto distributions; Pareto principle; Power; Probability: distributions; Stochastic Ordering; Stochastic orderings; Stochastic systems; Strength parameters; Stress strength; Stress-strength parameter; Stress-Strength Parameter; α-Power transformation; Α-power transformation
• Online Access: View Fulltext in Publisher

 The study focuses on the development of a new probability distribution with applications to extreme values. The distribution is proposed by incorporating an additional parameter into the inverse Pareto distribution using the α-Power Transformation. Various properties of the new distribution are derived. The paper also explores the estimation of the parameters by the Maximum Likelihood Estimation (MLE) technique. Simulations are performed to evaluate the performance of the MLEs. In addition, two real data sets with extreme values are used to evaluate the efficacy of the proposed model. It is concluded that the proposed model performs well in the case of extreme values compared to the existing distributions. © 2023 Shumaila Ihtisham et al., published by Sciendo.