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New Families of Generalized Lomax Distributions: Properties and Applications

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  • Ahmad Alzaghal
  • Duha Hamed

Abstract

In this paper, we propose new families of generalized Lomax distributions named T-LomaxfYg. Using the methodology of the Transformed-Transformer, known as T-X framework, the T-Lomax families introduced are arising from the quantile functions of exponential, Weibull, log-logistic, logistic, Cauchy and extreme value distributions. Various structural properties of the new families are derived including moments, modes and Shannon entropies. Several new generalized Lomax distributions are studied. The shapes of these T-LomaxfYg distributions are very flexible and can be symmetric, skewed to the right, skewed to the left, or bimodal. The method of maximum likelihood is proposed for estimating the distributions parameters and a simulation study is carried out to assess its performance. Four applications of real data sets are used to demonstrate the flexibility of T-LomaxfYg family of distributions in fitting unimodal and bimodal data sets from di erent disciplines.

Suggested Citation

  • Ahmad Alzaghal & Duha Hamed, 2019. "New Families of Generalized Lomax Distributions: Properties and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-51, November.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:6:p:51
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    References listed on IDEAS

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    1. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
    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. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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    Cited by:

    1. Sanaa Al-Marzouki & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2019. "Type II Topp Leone Power Lomax Distribution with Applications," Mathematics, MDPI, vol. 8(1), pages 1-26, December.
    2. Duha Hamed & Ahmad Alzaghal, 2021. "New class of Lindley distributions: properties and applications," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-22, December.
    3. Victor Korolev, 2023. "Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions," Mathematics, MDPI, vol. 11(13), pages 1-27, June.
    4. Adebisi Ade Ogunde & Victoria Eshomomoh Laoye & Ogbonnaya Nzie Ezichi & Kayode Oguntuase Balogun, 2021. "Harris Extended Power Lomax Distribution: Properties, Inference and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 1-77, July.

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