Abstract: Probability distributions serve as the building blocks for modeling various real-world phenomena, enabling researchers and practitioners to make informed decisions and predictions. Numerous research fields, including but not limited to engineering, environmental, medical, and financial studies, use probability distributions as probabilistic models. In this paper, we attempted to develop a quartic transmuted Fréchet (QTF) distribution from the general quartic transmutation family of distributions using Fréchet distribution as a baseline distribution. The distributive characteristics of the QTF distribution such as non-central moments, generating functions, reliability function, hazard rate function, and distributions of order statistics are discussed. The parameters of the QTF distribution are estimated by seven different estimation approaches as: maximum likelihood estimation method, two least squares based methods, maximum product of spacing method and three goodness of fit based estimation methods. A comprehensive simulation study is conducted to assess the efficiency of the estimators of the various methodologies mentioned. Regarding estimation methods, simulation outcomes indicated that all the methods except MLE in general performed outstanding in terms of estimation efficiency for large sample size, while all considered estimation methods performed almost same in terms of goodness of fit regardless the values of shape and transmuted parameters. Engineering and medical datasets were applied on the proposed distribution along with Fréchet, transmuted Fréchet, and cubic transmuted Fréchet distributions to compare the applicability and flexibility of the distributions. Anderson-Darling estimation (ADE) and right Anderson-Darling estimation (RADE) methods provided the best model fitting estimates of the proposed distribution for carbon fiber data and bladder cancer data, respectively. The proposed quartic transmuted Fréchet distribution provided significantly improved fit for the two datasets as compared with competing distributions.
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Keywords and phrases: Fréchet distribution, quartic transmuted family, parameter estimation, simulation.
Received: October 31, 2023; Accepted: December 2, 2023; Published: January 2, 2024
How to cite this article: Deluar J. Moloy, M. A. Ali and Farouq Mohammad A. Alam, Quartic transmuted Fréchet distribution: properties, estimation and applications, Advances and Applications in Statistics 91(2) (2024), 175-204. http://dx.doi.org/10.17654/0972361724012
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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