Arctan–Weibull Log Logistic Mixture Distribution: Theory and Applications to Lifetime Data

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DOI: https://doi.org/10.28924/2291-8639-24-2026-329
Published: Oct 5, 2026
Cite as:
K. E. Anyiam, C. P. Obite, N. C. Umelo-Ibenere, C. H. Izunobi, O. G. Nwafor, I. C. Obinwanne, O. G. Onukwube, L. C. Kiwu, E. O. Chukwudi, Arctan–Weibull Log Logistic Mixture Distribution: Theory and Applications to Lifetime Data, Int. J. Anal. Appl., 24 (2026), 329.

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K. E. Anyiam, C. P. Obite, N. C. Umelo-Ibenere, C. H. Izunobi, O. G. Nwafor, I. C. Obinwanne, O. G. Onukwube, L. C. Kiwu, E. O. Chukwudi

Abstract

This paper introduces the ArcTangent Weibull Log Logistic Mixture (AT-WLLM) distribution, a novel and flexible lifetime model constructed by applying an arctangent transformation to a mixture of Weibull and log-logistic distribution functions. The proposed model exhibits several desirable properties, including the ability to capture a wide range of hazard rate shapes commonly encountered in reliability engineering and survival analysis. The theoretical properties of the AT-WLLM distribution are thoroughly investigated. Parameter estimation is carried out using the maximum likelihood method, and a comprehensive simulation study is conducted to assess the performance of the estimators. Across all parameter configurations considered, the MLE procedure for the AT-WLLM distribution exhibits numerical stability and satisfactory finite–sample performance. The practical applicability of the model is demonstrated through three real-data analyses, in which the AT-WLLM distribution is compared with seven well-known competing models. The empirical results consistently affirm the superior flexibility and strength of the AT-WLLM distribution in modeling lifetime data.

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