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Unit-log-symmetric models: characterization, statistical properties and their applications to analyzing an internet access data

Author

Listed:
  • Roberto Vila

    (University of Brasília
    McMaster University)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Helton Saulo

    (University of Brasília
    University of Texas at Arlington)

  • Peter Zörnig

    (University of Brasília)

Abstract

We present here a unit-log-symmetric model based on the bivariate log-symmetric distribution discussed in recent literature. It is a flexible family of distributions over the interval (0, 1). We then discuss its mathematical properties such as stochastic representation, identifiability, symmetry, modality, moments, quantile function, entropy and maximum likelihood estimation, paying particular attention to the special cases of unit-log-normal, unit-log-Student-t and unit-log-Laplace distributions. Finally, some empirical results and a real-life data analysis involving internet acess data are presented for illustrative purpose.

Suggested Citation

  • Roberto Vila & Narayanaswamy Balakrishnan & Helton Saulo & Peter Zörnig, 2024. "Unit-log-symmetric models: characterization, statistical properties and their applications to analyzing an internet access data," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4779-4806, October.
    • Handle: RePEc:spr:qualqt:v:58:y:2024:i:5:d:10.1007_s11135-024-01879-w
    DOI: 10.1007/s11135-024-01879-w
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    References listed on IDEAS

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    2. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
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