A New Zero-Truncated Version of the Poisson Burr XII Distribution: Characterizations and Properties

Yousof, Haitham M.; Ahsanullah, Mohammad; Khalil, Mohamed G.

doi:10.2991/jsta.d.190306.001

Cited by 13 publications

(9 citation statements)

References 22 publications

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“…Their exploration encompassed a comprehensive analysis of various aspects, including characterizations, order statistics, ordinary and incomplete moments, residual and reversed residual life functions, and the moment generating function associated with this distribution. This investigation by Yousof et al [58] represents a pivotal contribution to the statistical literature, shedding light on the intricacies and potential applications of the PTL-BXII distribution. By systematically elucidating its theoretical foundations and exploring its mathematical properties, their study has provided valuable insights that facilitate a deeper understanding of this specialized model.…”

Section: Introductionmentioning

confidence: 92%

“…Notably, Yousof et al introduced a novel variant of this model, termed the Poisson Topp-Leone Burr XII (PTL-BXII) distribution, which has garnered considerable attention. In their study, Yousof et al [58] delved deep into the theoretical underpinnings and mathematical properties of the PTL-BXII distribution. Their exploration encompassed a comprehensive analysis of various aspects, including characterizations, order statistics, ordinary and incomplete moments, residual and reversed residual life functions, and the moment generating function associated with this distribution.…”

Section: Introductionmentioning

confidence: 99%

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Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications

Khalil,

Aidi,

Ali

et al. 2024

Stat., optim. inf. comput.

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The Poisson Topp Leone Burr XII distribution is extensively studied due to its broad relevance in analyzing censored real datasets from engineering, economics, and medicine. In this research, the distribution's versatility is highlighted through the analysis of four specific real datasets. The study compares the Poisson Topp Leone Burr XII distribution with nine extensions of the Burr type XII distribution to determine which offers the best fit for these datasets. To evaluate the goodness-of-fit of the Poisson Topp Leone Burr XII distribution under right censoring, a modified Bagdonavi\v{c}ius-Nikulin goodness-of-fit test statistic is introduced and applied. This new test statistic is utilized to validate the distributional fit for the Poisson Topp Leone Burr XII distribution across the four right-censored datasets. The modified Bagdonavi\v{c}ius-Nikulin test statistic is employed to assess distributional validation, specifically in the context of right censoring. The application of this statistic involves analyzing each of the four censored datasets to confirm the appropriateness of the Poisson Topp Leone Burr XII distribution for these scenarios. Additionally, to support the evaluation of the modified goodness-of-fit test statistic, the Barzilai-Borwein algorithm is utilized. This algorithm is employed within a simulation study to further assess the effectiveness and reliability of the modified Bagdonavi\v{c}ius-Nikulin test statistic, thereby ensuring robust validation of the Poisson Topp Leone Burr XII distribution against the observed real datasets.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications

Khalil,

Aidi,

Ali

et al. 2024

Stat., optim. inf. comput.

View full text Add to dashboard Cite

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“…Publications such as Mansour et al [16], Elbiely and Yousof [7], Ibrahim and Yousof [6], Aryal et al [28], Yousof et al [29,30], Yadav et al [8], and Goual et al [31,32] are just a few examples of studies that include many other useful real-life datasets. A non-parametric technique called kernel density estimation (KDE) is used to calculate the probability density function of a random variable from a set of observations.…”

Section: Second Datasetmentioning

confidence: 99%

Flexible Extension of the Lomax Distribution for Asymmetric Data under Different Failure Rate Profiles: Characteristics with Applications for Failure Modeling and Service Times for Aircraft Windshields

et al. 2023

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A novel four-parameter lifetime Lomax model is presented and investigated within the scope of this paper. The failure rate of the innovative model can be “monotonically decreasing failure rate,” “monotonically increasing failure rate,” or “constant failure rate,” and the density of the model can be “asymmetric right skewed,” “symmetric,” “asymmetric left skewed,” or “uniform density”. The new density is expressed as a blend of the Lomax densities that have been multiplied by an exponent. New bivariate Lomax types were created for our research. The maximum likelihood technique was utilized. We performed simulated experiments for the purpose of evaluating the finite sample behavior of maximum likelihood estimators, using “biases” and “mean squared errors” as our primary metrics of analysis. The novel distribution was evaluated based on a number of pertinent Lomax models, including Lomax extensions that were generated on the basis of odd log-logistic, Kumaraswamy, beta, gamma, and Topp–Leone families, among others. The newly developed extension demonstrated its relevance by predicting the service and failure times of datasets pertaining to aircraft windshields.

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“…Further, the above two parameter Lx model is a special case from the well-known Burr type XII (B (XII)) model, so several properties of the Lx model can be easily obtained from the B (XII) model (for more details about the relation between the Lx model and the B (XII) model see [2][3][4][5][6][7][8]). Many generalizations of the Lx model were recently proposed and studied such as the exponentiated Lx (ExpLx) and Marshall-Olkin extended Lx (MOExLx) by [9,10], beta Lx (BLx) and gamma Lx (GamLx) by [11,12], the Weibull Lx (WLx) and transmuted WLx (TWLx) by [13,14], Weibull Generalized Lx (WGLx) and odd Lindley Lx (OLiLx) by [15,16], Zografos-Balakrishnan Lx (ZBLx) by [17], Poisson-Topp Leone Lx (PTLLx) by [18], Burr XII Lx (BXIILx) by [19], and the two parameter Topp Leone Lx (2PTLLx) by [20], among others.…”

Section: Introductionmentioning

confidence: 99%

Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation

et al. 2019

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In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose.

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A New Zero-Truncated Version of the Poisson Burr XII Distribution: Characterizations and Properties

Cited by 13 publications

References 22 publications

Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications

Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications

Flexible Extension of the Lomax Distribution for Asymmetric Data under Different Failure Rate Profiles: Characteristics with Applications for Failure Modeling and Service Times for Aircraft Windshields

Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation

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