Applied Statistical Modeling Using the Truncated Perk Distribution: Estimation Methods and Multidisciplinary Real-Data Applications

In this paper, we propose a new version of the Perk distribution, called the truncated Perk distribution. Fundamental properties of the new distribution are discussed, including moments, the moment generating function, the probability-weighted function, the quantile function, order statistics, Rényi entropy, and Tsallis entropy. In practice, for the estimation of the model parameters, we use seven traditional estimation methods. A simulation study was performed to demonstrate the practical utility of the proposed distribution. In this study, two common estimation methods, MLE and Bayesian estimation, are compared to determine which method provides more accurate and reliable parameter estimates. The potential utility of the truncated Perk model is exhibited through its use on three real datasets. The applications indicate that the truncated Perk distribution can give better fits than some other corresponding distributions.