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Abstract

Despite significant progress in the development of statistical distributions, there remain clear gaps in modelling complex datasets, such as those involving uncertainty or requiring flexible representations of multidimensional variables. This study introduces a new distribution the Neutrosophic Gompertz-Inverse Burr-X (NGoIB-X) distribution to address these challenges. The model is based on the Neutrosophic Gompertz family (NGo-G), which itself employs the T-X method in its formulation. Characterised by four Neutrosophic parameters and a Neutrosophic random variable, the NGoIB-X distribution offers enhanced flexibility for representing and analysing uncertain data. The theoretical properties of the NGoIB-X distribution are explored, including its Neutrosophic probability density function (NPDF), Neutrosophic cumulative distribution function (NCDF), and hazard function. Parameters estimation is conducted using three methods: maximum likelihood estimation (MLE), least squares (LS), and weighted least squares (WLS). A Monte Carlo simulation is performed to evalute the efficiency of these estimation techniques. To demonstrate practical relevance, the NGoIB-X distribution is applied to Neutrosophic data on under-five mortality rates. The proposed model achieved lowr values across model selection criteria AIC: [177.437, 177.531]; CAIC: [179.342, 179.435]; BIC: [182.470, 182.563]; HQIC: [178.887, 178.9802] compared to five alternative distributions. These results highlight the distribution's effectiveness in accurately representing complex datasets, confirming its suitability for applications in public health and applied statistics.

Reason for Retraction

This article has been retracted at the request of the Editorial Office, following an internal investigation conducted in accordance with the Committee on Publication Ethics (COPE) Retraction Guidelines.

The investigation identified serious concerns affecting the integrity and reliability of the published work. Specifically, one or more of the following issues were confirmed:

  1. Undisclosed use of computer-generated text and/or data, in which substantial portions of the content were produced using algorithmic or artificial intelligence–based tools without transparent disclosure, contrary to the journal's authorship and transparency policies.

  2. Compromised peer-review process, indicating irregularities that undermine the validity, independence or authenticity of the review procedure.

  3. Inappropriate or misleading citations, including references that are irrelevant, improperly used, or appear to artificially inflate citation metrics, thereby distorting the scholarly record.

  4. Authorship-related concerns, including the addition of new author(s) at a later stage of the publication process without adequate justification, documentation, or transparent disclosure, raising unresolved questions regarding author contributions, responsibility, and compliance with the journal's authorship criteria.

The Editorial Office determined that these issues significantly compromise the scientific integrity of the article, and that correction alone would be insufficient to address the concerns. Retraction was therefore deemed necessary to maintain the accuracy and trustworthiness of the scholarly record.

The authors were informed of the findings and the retraction decision. While the authors do not respond to this retraction, the journal has proceeded with the retraction in line with COPE guidance, which permits retraction without author consent when editorial integrity is at risk.

This retraction is issued to alert readers that the findings and conclusions of the article should not be relied upon. The original article will remain accessible for the sake of the scholarly record, but it will be clearly marked as retracted.

Apologies are offered to readers of the journal that this was not detected during the submission process.

Please see the Retraction Notice available at: https://ijcsm.researchcommons.org/ijcsm/vol6/iss3/23

DOI: https://doi.org/10.52866/2788-7421.1371

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