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A Logistic Trigonometric Generalized Class of Distribution Characteristics, Applications, and Simulations

Author

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  • Zafar Mahmood
  • Hazar A. Khogeer
  • Eslam Hussam Hafez
  • Md. Moyazzem Hossain

Abstract

We propose a trigonometric generalizer/generator of distributions utilizing the quantile function of modified standard Cauchy distribution and construct a logistic‐based new G‐class disbursing cotangent function. Significant mathematical characteristics and special models are derived. New mathematical transformations and extended models are also proposed. A two‐parameter model logistic cotangent Weibull (LCW) is developed and discussed in detail. The beauty and importance of the proposed model are that its hazard rate exhibits all monotone and non‐monotone shapes while the density exhibits unimodal and bimodal (symmetrical, right‐skewed, and decreasing) shapes. For parametric estimation, the maximum likelihood approach is used, and simulation analysis is performed to ensure that the estimates are asymptotic. The importance of the proposed trigonometric generalizer, G class, and model is proved via two applications focused on survival and failure datasets whose results attested the distinct better fit, wider flexibility, and greater capability than existing and well‐known competing models. The authors thought that the suggested class and models would appeal to a broader audience of professionals working in reliability analysis, actuarial and financial sciences, and lifetime data and analysis.

Suggested Citation

  • Zafar Mahmood & Hazar A. Khogeer & Eslam Hussam Hafez & Md. Moyazzem Hossain, 2022. "A Logistic Trigonometric Generalized Class of Distribution Characteristics, Applications, and Simulations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7091581
    DOI: 10.1155/2022/7091581
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    References listed on IDEAS

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    1. El-Sayed A. El-Sherpieny & Mamhoud M. Elsehetry, 2019. "Type II Kumaraswamy Half Logistic Family of Distributions with Applications to Exponential Model," Annals of Data Science, Springer, vol. 6(1), pages 1-20, March.
    2. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    3. Emrah Altun & Mustafa Ç. Korkmaz & Mahmoud El-Morshedy & Mohamed S. Eliwa, 2021. "A New Flexible Family of Continuous Distributions: The Additive Odd-G Family," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
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