Search Results (4)

This paper introduces a q-deformed extension of the Lindley distribution. This extension is obtained by replacing the classical exponential with the q-exponential function from Tsallis non-extensive statistical techniques. This transformation offers more control over the tail behavior of the distribution, providing a transition between exponential and power-law decay patterns. Such flexibility is particularly useful when modeling right-skewed data with excess kurtosis, where classical models may not adequately describe heavy-tailed and highly skewed data. We derive several key properties, including the quantile function, expressed by the Lambert–Tsallis function Wq, the raw and incomplete moments, the probability-weighted moments, and the Tsallis entropy. The distribution of order statistics is also investigated. For parameter estimation, we employ several frequentist methods and conduct extensive Monte Carlo simulation studies to assess and compare their performance. Finally, applications to real-world datasets show that the q-deformed Lindley model is practically superior and more flexible than the classical Lindley distribution and other well-known models. Full article

This paper presents a new model that surpasses traditional distributions, specifically the three-parameter distribution of the Inverse Power Entropy Chen (IPEC) model. In comparison to the existing distributions, the latest one presents an exceptionally diverse array of probability functions. The density and hazard rate functions have characteristics indicating that the model is adaptable to many types of data. The study explores the mathematical features of the IPEC distribution, including moments with some related measures, quantile function, Rényi entropy, Tsallis entropy, and order statistics. To estimate the parameters of the IPEC model, we utilized seven classical estimation strategies, including maximum likelihood estimators, Anderson–Darling estimators, right-tail Anderson–Darling estimators, Cramér–von Mises estimators, percentile estimators, least-squares estimators, and weighted least-squares estimators. To evaluate the efficacy of these estimating approaches across varying sample sizes, Monte Carlo simulations are performed. The efficacy of each estimator is evaluated through comparisons of average relative bias and mean squared error, highlighting their suitability for the used samples. Three applications utilize real-world datasets related to medical and physical fields, demonstrating the usefulness of the new model in relation to several established competitive models. This empirical investigation further supports the utility and adaptability of the inverse power entropy Chen model in capturing the intricacies of distinct datasets, hence delivering useful insights for practitioners in numerous domains. Full article

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. Full article

With the help of Tsallis residual entropy, we introduce Tsallis quantile entropy order between two random variables. We give necessary and sufficient conditions, study closure and reversed closure properties under parallel and series operations and show that this order is preserved in the proportional hazard rate model, proportional reversed hazard rate model, proportional odds model and record values model. Full article