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On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications

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  • Maria T. Vasileva

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria)

Abstract

This paper discusses the Topp-Leone-G power series class of distributions. The greatest attention is paid to the investigation of intrinsic characteristic “saturation” to the horizontal asymptote in the Hausdorff sense. Some estimates for the value of the Hausdorff distance are obtained. We present a new family of recurrence generated adaptive functions with corresponding applications. The usefulness of the obtained results is demonstrated in a simulation study of some real data sets from the medical sector and insurance. Some suitable software modules within the programming environment CAS MATHEMATICA are proposed.

Suggested Citation

  • Maria T. Vasileva, 2023. "On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications," Mathematics, MDPI, vol. 11(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4620-:d:1278291
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    References listed on IDEAS

    as
    1. Broderick Oluyede & Neo Dingalo & Fastel Chipepa, 2023. "The Topp-Leone-Harris-G family of distributions with applications," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 24(4), pages 554-582.
    2. Nikolay Kyurkchiev, 2020. "Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    3. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    4. Suleman Nasiru & Peter N. Mwita & Oscar Ngesa, 2019. "Exponentiated Generalized Power Series Family of Distributions," Annals of Data Science, Springer, vol. 6(3), pages 463-489, September.
    5. Sadegh Rezaei & Behnam Bahrami Sadr & Morad Alizadeh & Saralees Nadarajah, 2017. "Topp–Leone generated family of distributions: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(6), pages 2893-2909, March.
    6. Zubair Ahmad & Eisa Mahmoudi & Gholamhossien Hamedani, 2022. "A class of claim distributions: Properties, characterizations and applications to insurance claim data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(7), pages 2183-2208, April.
    7. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    8. A. A. Jafari & S. Tahmasebi, 2016. "Gompertz-power series distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3761-3781, July.
    9. Mustapha Muhammad & Lixia Liu & Badamasi Abba & Isyaku Muhammad & Mouna Bouchane & Hexin Zhang & Sani Musa, 2023. "A New Extension of the Topp–Leone-Family of Models with Applications to Real Data," Annals of Data Science, Springer, vol. 10(1), pages 225-250, February.
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