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A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems

Author

Listed:
  • Ibrahim Alkhairy
  • Humaira Faqiri
  • Zubir Shah
  • Hassan Alsuhabi
  • M. Yusuf
  • Ramy Aldallal
  • Nicholas Makumi
  • Fathy H. Riad

Abstract

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic‐X (NFLog‐X) family. The suggested NFLog‐X family is obtained by applying the T‐X method together with the exponential model having the PDF m(t) = e−t. Based on the NFLog‐X approach, a three parameters probability distribution, namely, a new flexible logarithmic‐Weibull (NFLog‐Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog‐X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog‐Wei distribution. Comparisons are made between the analytical goodness‐of‐fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic‐Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

Suggested Citation

  • Ibrahim Alkhairy & Humaira Faqiri & Zubir Shah & Hassan Alsuhabi & M. Yusuf & Ramy Aldallal & Nicholas Makumi & Fathy H. Riad, 2022. "A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:7845765
    DOI: 10.1155/2022/7845765
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    References listed on IDEAS

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    1. Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    2. Wanting Wang & Zubair Ahmad & Omid Kharazmi & Clement Boateng Ampadu & E H Hafez & Marwa M Mohie El-Din, 2021. "New generalized-X family: Modeling the reliability engineering applications," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-26, March.
    3. Xiaoyan Huo & Saima K. Khosa & Zubair Ahmad & Zahra Almaspoor & Muhammad Ilyas & Muhammad Aamir, 2020. "A New Lifetime Exponential- X Family of Distributions with Applications to Reliability Data," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, August.
    4. 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.
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