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

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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.

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) (Finance Code 001). Roberto Vila gratefully acknowledges financial support from FAP-DF, Brazil.

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Authors and Affiliations

  1. Department of Statistics, University of Brasília, Brasília, Brazil

    Roberto Vila, Helton Saulo & Peter Zörnig

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Roberto Vila & Narayanaswamy Balakrishnan

  3. Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA

    Helton Saulo

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  1. Roberto Vila
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  2. Narayanaswamy Balakrishnan
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  3. Helton Saulo
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  4. Peter Zörnig
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Correspondence to Roberto Vila.

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Vila, R., Balakrishnan, N., Saulo, H. et al. Unit-log-symmetric models: characterization, statistical properties and their applications to analyzing an internet access data. Qual Quant 58, 4779–4806 (2024). https://doi.org/10.1007/s11135-024-01879-w

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