Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

A novel discrete exponentiated Chen (DEC) distribution, which is a subset of the continuous exponentiated Chen distribution, is proposed. The offered model is more adaptable to analyzing a wide range of data than traditional and recently published models. Several important statistical and reliability characteristics of the DEC model are introduced. In the presence of Type-II censored data, the maximum likelihood and asymptotic confidence interval estimators of the model parameters are acquired. Two various bootstrapping estimators of the DEC parameters are also obtained. To examine the efficacy of the adopted methods, several simulations are implemented. To further clarify the offered model in the life scenario, the two applications, based on the number of vehicle fatalities in South Carolina in 2012 and the final exam marks in 2004 at the Indian Institute of Technology at Kanpur, are analyzed. The analysis findings showed that the DEC model is the most effective model for fitting the supplied data sets compared to eleven well-known models in literature, including: Poisson, geometric, negative binomial, discrete-Weibull, discrete Burr Type XII, discrete generalized exponential, discrete-gamma, discrete Burr Hatke, discrete Nadarajah-Haghighi, discrete modified-Weibull, and exponentiated discrete-Weibull models. Ultimately, the new model is recommended to be applied in many fields of real practice.

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“…Notably, ref. [27] investigated various inferential approaches for the exponentiated discrete Weibull model with censored data.…”

Section: Introductionmentioning

confidence: 99%

The Discrete Exponentiated-Chen Model and Its Applications

et al. 2023

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“…However, a few studies considered this censoring scheme for discrete models, viz. Krishna and Goel [25], de Oliveira et al [26], and most recently, Achcar et al [27] discussed classical and Bayesian inference of exponentiated discrete Weibull distribution with censored data. Moreover, most of the existing discrete models were developed to analyze count data and in most situations, they fail to capture the diversity of the censored data.…”

Section: Introductionmentioning

confidence: 99%

Discrete Inverted Nadarajah-Haghighi Distribution: Properties and Classical Estimation with Application to Complete and Censored data

Singh

Nayal

et al. 2022

Stat., optim. inf. comput.

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In this article, we have developed the discrete version of the continuous inverted Nadarajah-Haghighi distribution and called it a discrete inverted Nadarajah-Haghighi distribution. The present model is well enough to model not only the over-dispersed and positively skewed data but it can also model upside-down bathtub-shaped, decreasing failure rate, and randomly right-censored data. Here, we have developed some important statistical properties for the proposed model such as quantile, median, moments, skewness, kurtosis, index of dispersion, entropy, expected inactivity time function, stress-strength reliability, and order statistics. We have estimated the model parameters through the method of maximum likelihood under complete and censored data. An algorithm to generate randomly right-censored data from the proposed model is also presented. The extensive simulation studies are presented to test the behavior of the estimators with complete and censored data. Finally, two complete and two censored data are used to illustrate the utility of the proposed model.

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