IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i3p667-d1049583.html
   My bibliography  Save this article

An Alternative Lambert-Type Distribution for Bounded Data

Author

Listed:
  • Héctor Varela

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Mario A. Rojas

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Jimmy Reyes

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Yuri A. Iriarte

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

Abstract

In this article, we propose a new two-parameter distribution for bounded data such as rates, proportions, or percentages. The density function of the proposed distribution, presenting monotonic, unimodal, and inverse-unimodal shapes, tends to a positive finite value at the lower end of its support, which can lead to a better fit of the lower empirical quantiles. We derive some of the main structural properties of the new distribution. We make a description of the skewness and kurtosis of the distribution. We discuss the parameter estimation under the maximum likelihood method. We developed a simulation study to evaluate the behavior of the estimators. Finally, we present two applications to real data providing evidence that the proposed distribution can perform better than the popular beta and Kumaraswamy distributions.

Suggested Citation

  • Héctor Varela & Mario A. Rojas & Jimmy Reyes & Yuri A. Iriarte, 2023. "An Alternative Lambert-Type Distribution for Bounded Data," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:667-:d:1049583
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/3/667/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/3/667/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuri A. Iriarte & Mário de Castro & Héctor W. Gómez, 2020. "The Lambert- F Distributions Class: An Alternative Family for Positive Data Analysis," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    2. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
    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. Tue Gørgens & Allan Würtz, 2012. "Testing a parametric function against a non‐parametric alternative in IV and GMM settings," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 462-489, October.
    2. Erich Battistin & Raffaele Miniaci & Guglielmo Weber, 2003. "What Do We Learn from Recall Consumption Data?," Journal of Human Resources, University of Wisconsin Press, vol. 38(2).
    3. Blow, Laura & Crawford, Ian, 2002. "A nonparametric method for valuing new goods," Working Paper Series 143, European Central Bank.
    4. Thanasis Stengos & Yiguo Sun & Dianqin Wang, 2006. "Estimates of semiparametric equivalence scales," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 629-639, July.
    5. Missong, Martin & Rolf, Anja, 2004. "Utility based regional purchasing power parities," FE Working Papers 0403, Christian-Albrechts-University of Kiel, Department of Food Economics and Consumption Studies.
    6. Thomas F. Crossley & Krishna Pendakur, 2002. "Consumption Inequality," Department of Economics Working Papers 2002-09, McMaster University.
    7. Lewbel, Arthur & Pendakur, Krishna, 2008. "Estimation of collective household models with Engel curves," Journal of Econometrics, Elsevier, vol. 147(2), pages 350-358, December.
    8. Stengos, T. & Lyssiotou, P. & Pashardes, P., 2002. "Demographic vs. Expenditure Flexibility in Engel Curves," Working Papers 2002-15, University of Guelph, Department of Economics and Finance.
    9. Farrell, Lisa & Shields, Michael A., 2001. "Child Expenditure: The Role of Working Mothers, Lone Parents, Sibling Composition and Household Provision," IZA Discussion Papers 388, Institute of Labor Economics (IZA).
    10. Mark B. Stewart, 2009. "The Estimation Of Pensioner Equivalence Scales Using Subjective Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(4), pages 907-929, December.
    11. Ingvild Almas, 2012. "International Income Inequality: Measuring PPP Bias by Estimating Engel Curves for Food," American Economic Review, American Economic Association, vol. 102(2), pages 1093-1117, April.
    12. Xin Meng & Xiaodong Gong & Youjuan Wang, 2009. "Impact of Income Growth and Economic Reform on Nutrition Availability in Urban China: 1986-2000," Economic Development and Cultural Change, University of Chicago Press, vol. 57(2), pages 261-295, January.
    13. Takashi Unayama, 2006. "The Engel curve for alcohol and the rank of demand systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1019-1038, November.
    14. Tey, (John) Yeong-Sheng & Shamsudin, Mad Nasir & Mohamed, Zainalabidin & Abdullah, Amin Mahir & Radam, Alias, 2009. "Evidence of Engel curves in food away from home: A study of Malaysia," MPRA Paper 14833, University Library of Munich, Germany.
    15. Lamichhane, Kamal & Sawada, Yasuyuki, 2013. "Disability and returns to education in a developing country," Economics of Education Review, Elsevier, vol. 37(C), pages 85-94.
    16. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    17. repec:cep:stiecm:/2011/557 is not listed on IDEAS
    18. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    19. Orazio Attanasio & Erich Battistin & Alice Mesnard, 2012. "Food and Cash Transfers: Evidence from Colombia," Economic Journal, Royal Economic Society, vol. 122(559), pages 92-124, March.
    20. Mette Christensen, 2007. "Integrability of Demand Accounting for Unobservable Heterogeneity: A Test on Panel Data," Economics Discussion Paper Series 0713, Economics, The University of Manchester.
    21. Gong, X. & van Soest, A.H.O. & Zhang, P., 2000. "Sexual Bias and Household Consumption : A Semiparametic Analysis of Engel curves in Rural China," Other publications TiSEM 896cf4d1-37e5-490b-9e05-4, Tilburg University, School of Economics and Management.

    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:3:p:667-:d:1049583. 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.