IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1398-d401993.html
   My bibliography  Save this article

The Lambert- F Distributions Class: An Alternative Family for Positive Data Analysis

Author

Listed:
  • Yuri A. Iriarte

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

  • Mário de Castro

    (Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, SP, Brazil)

  • Héctor W. Gómez

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

In this article, we introduce a new probability distribution generator called the Lambert- F generator. For any continuous baseline distribution F , with positive support, the corresponding Lambert- F version is generated by using the new generator. The result is a new class of distributions with one extra parameter that generalizes the baseline distribution and whose quantile function can be expressed in closed form in terms of the Lambert W function. The hazard rate function of a Lambert- F distribution corresponds to a modification of the baseline hazard rate function, greatly increasing or decreasing the baseline hazard rate for earlier times. Herein, we study the main structural properties of the new class of distributions. Special attention is given to two particular cases that can be understood as two-parameter extensions of the well-known exponential and Rayleigh distributions. We discuss parameter estimation for the proposed models considering the moments and maximum likelihood methods. Finally, two applications were developed to illustrate the usefulness of the proposed distributions in the analysis of data from different real settings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1398-:d:401993
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1398/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1398/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. C.D. Lai, 2013. "Constructions and applications of lifetime distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(2), pages 127-140, March.
    2. Saralees Nadarajah & Samuel Kotz, 2004. "The beta Gumbel distribution," Mathematical Problems in Engineering, Hindawi, vol. 2004, pages 1-10, January.
    3. Essam AL-Hussaini, 2010. "Inference based on censored samples from exponentiated populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 487-513, November.
    4. Matt Visser, 2018. "Primes and the Lambert W function," Mathematics, MDPI, vol. 6(4), pages 1-6, April.
    5. 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.
    6. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
    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. 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.

    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. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    2. 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.
    3. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    4. Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    5. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2020. "On a New Result on the Ratio Exponentiated General Family of Distributions with Applications," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    6. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    7. Carol Alexander & José María Sarabia, 2012. "Quantile Uncertainty and Value‐at‐Risk Model Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1293-1308, August.
    8. Iliev, A. & Kyurkchiev, N. & Markov, S., 2017. "On the approximation of the step function by some sigmoid functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 223-234.
    9. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    10. 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.
    11. Ghosh Indranil, 2019. "On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 115-121, December.
    12. Abdus Saboor & Muhammad Nauman Khan & Gauss M. Cordeiro & Marcelino A. R. Pascoa & Juliano Bortolini & Shahid Mubeen, 2019. "Modified beta modified-Weibull distribution," Computational Statistics, Springer, vol. 34(1), pages 173-199, March.
    13. Robert King & Irene Lena Hudson & Muhammad Shuaib Khan, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 183-210, June.
    14. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    15. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    16. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.
    17. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
    18. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    19. 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.
    20. 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.

    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:8:y:2020:i:9:p:1398-:d:401993. 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.