IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2634-d660274.html
   My bibliography  Save this article

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

Author

Listed:
  • Mustafa Ç. Korkmaz

    (Department of Measurement and Evaluation, Artvin Çoruh University, City Campus, 08000 Artvin, Turkey)

  • Emrah Altun

    (Department of Mathematics, Bartin University, 74000 Bartin, Turkey)

  • Morad Alizadeh

    (Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran)

  • M. El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

Recently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2634-:d:660274
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2634/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/21/2634/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
    3. 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.
    4. Josmar Mazucheli & André Felipe Menezes & Sanku Dey, 2019. "Unit-Gompertz Distribution with Applications," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 25-43.
    5. Emrah Altun & Gauss M. Cordeiro, 2020. "The unit-improved second-degree Lindley distribution: inference and regression modeling," Computational Statistics, Springer, vol. 35(1), pages 259-279, March.
    6. 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.
    7. 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.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.

    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. 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.
    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. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    4. 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.
    5. Artur J. Lemonte & Germán Moreno-Arenas, 2020. "On a heavy-tailed parametric quantile regression model for limited range response variables," Computational Statistics, Springer, vol. 35(1), pages 379-398, March.
    6. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2021. "Theory and Applications of the Unit Gamma/Gompertz Distribution," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    7. Yayan Hernuryadin & Koji Kotani & Tatsuyoshi Saijo, 2020. "Time Preferences of Food Producers: Does “Cultivate and Grow” Matter?," Land Economics, University of Wisconsin Press, vol. 96(1), pages 132-148.
    8. Jodrá, P. & Jiménez-Gamero, M.D., 2016. "A note on the Log-Lindley distribution," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 189-194.
    9. 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.
    10. Müller, Alfred & Reuber, Matthias, 2023. "A copula-based time series model for global horizontal irradiation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 869-883.
    11. Terezinha K. A. Ribeiro & Silvia L. P. Ferrari, 2023. "Robust estimation in beta regression via maximum L $$_q$$ q -likelihood," Statistical Papers, Springer, vol. 64(1), pages 321-353, February.
    12. Souza, Tatiene C. & Cribari–Neto, Francisco, 2018. "Intelligence and religious disbelief in the United States," Intelligence, Elsevier, vol. 68(C), pages 48-57.
    13. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    14. Suelena S. Rocha & Patrícia L. Espinheira & Francisco Cribari‐Neto, 2021. "Residual and local influence analyses for unit gamma regressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 137-160, May.
    15. 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.
    16. Emrah Altun & Gauss M. Cordeiro, 2020. "The unit-improved second-degree Lindley distribution: inference and regression modeling," Computational Statistics, Springer, vol. 35(1), pages 259-279, March.
    17. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Waleed Almutiry & Amani Abdullah Alahmadi, 2021. "Study of a Modified Kumaraswamy Distribution," Mathematics, MDPI, vol. 9(21), pages 1-26, November.
    18. Diego I. Gallardo & Marcelo Bourguignon & Yolanda M. Gómez & Christian Caamaño-Carrillo & Osvaldo Venegas, 2022. "Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    19. David E. Giles, 2024. "New Goodness-of-Fit Tests for the Kumaraswamy Distribution," Stats, MDPI, vol. 7(2), pages 1-16, April.
    20. Akosah, Nana Kwame & Alagidede, Imhotep Paul & Schaling, Eric, 2020. "Testing for asymmetry in monetary policy rule for small-open developing economies: Multiscale Bayesian quantile evidence from Ghana," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).

    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:9:y:2021:i:21:p:2634-:d:660274. 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.