IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2888-d1180894.html
   My bibliography  Save this article

Unit Distributions: A General Framework, Some Special Cases, and the Regression Unit-Dagum Models

Author

Listed:
  • Francesca Condino

    (Department of Economics, Statistics and Finance “Giovanni Anania”, University of Calabria, Via P. Bucci, Cubo 0C, 87036 Rende, CS, Italy)

  • Filippo Domma

    (Department of Economics, Statistics and Finance “Giovanni Anania”, University of Calabria, Via P. Bucci, Cubo 0C, 87036 Rende, CS, Italy)

Abstract

In this work, we propose a general framework for models with support in the unit interval, which is obtained using the technique of random variable transformations. For this class, the general expressions of distribution and density functions are given, together with the principal characteristics, such as quantiles, moments, and hazard and reverse hazard functions. It is possible to verify that different proposals already present in the literature can be seen as particular cases of this general structure by choosing a suitable transformation. Moreover, we focus on the class of unit-Dagum distributions and, by specifying two different kinds of transformations, we propose the type I and type II unit-Dagum distributions. For these two models, we first consider the possibility of expressing the distribution in terms of indicators of interest, and then, through the regression approach, relate the indicators and covariates. Finally, some applications using data on the unit interval are reported.

Suggested Citation

  • Francesca Condino & Filippo Domma, 2023. "Unit Distributions: A General Framework, Some Special Cases, and the Regression Unit-Dagum Models," Mathematics, MDPI, vol. 11(13), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2888-:d:1180894
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2888/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2888/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Mazucheli & A. F. B. Menezes & L. B. Fernandes & R. P. de Oliveira & M. E. Ghitany, 2020. "The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 954-974, April.
    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.
    3. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    4. Suleman Nasiru & Abdul Ghaniyyu Abubakari & Irene Dekomwine Angbing & Sergejs Solovjovs, 2021. "Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2021, pages 1-18, May.
    5. Peter Xue-Kun Song & Ming Tan, 2000. "Marginal Models for Longitudinal Continuous Proportional Data," Biometrics, The International Biometric Society, vol. 56(2), pages 496-502, June.
    6. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    7. 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.
    8. Emrah Altun, 2021. "The log-weighted exponential regression model: alternative to the beta regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(10), pages 2306-2321, May.
    9. Emrah Altun & M El-Morshedy & M S Eliwa, 2021. "A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-15, January.
    10. Domma, Filippo & Condino, Francesca & Giordano, Sabrina, 2018. "A new formulation of the Dagum distribution in terms of income inequality and poverty measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 104-126.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    2. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    3. Abdul Ghaniyyu Abubakari & Suleman Nasiru & Christophe Chesneau, 2024. "A unit Weibull loss distribution with quantile regression and practical applications to actuarial science," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 1-29.
    4. Ricardo Rasmussen Petterle & Wagner Hugo Bonat & Cassius Tadeu Scarpin, 2019. "Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 346-368, June.
    5. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    6. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    7. Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    8. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa Ç. Korkmaz & Munir Ahmad, 2018. "The transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-23, December.
    9. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    10. Mehrzad Ghorbani & Seyed Fazel Bagheri & Mojtaba Alizadeh, 2017. "A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications," Annals of Data Science, Springer, vol. 4(2), pages 249-287, June.
    11. Zubair Ahmad, 2019. "The Hyperbolic Sine Rayleigh Distribution with Application to Bladder Cancer Susceptibility," Annals of Data Science, Springer, vol. 6(2), pages 211-222, June.
    12. Fábio Prataviera & Aline Martineli Batista & Edwin M. M. Ortega & Gauss M. Cordeiro & Bruno Montoani Silva, 2023. "The Logit Exponentiated Power Exponential Regression with Applications," Annals of Data Science, Springer, vol. 10(3), pages 713-735, June.
    13. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.
    14. Festus C. Opone & Christophe Chesneau, 2024. "The Opone family of distributions. Beyond the power continuous Bernoulli distribution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 103-124.
    15. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
    16. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    17. Ahmed M. T. Abd El-Bar & Willams B. F. da Silva & Abraão D. C. Nascimento, 2021. "An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data," Mathematics, MDPI, vol. 9(23), pages 1-15, December.
    18. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    19. 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.
    20. Vlad Stefan Barbu & Alex Karagrigoriou & Andreas Makrides, 2021. "Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case," Mathematics, MDPI, vol. 9(16), pages 1-17, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2888-:d:1180894. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.