IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i1d10.1007_s11009-024-10131-9.html
   My bibliography  Save this article

A New Family of Continuous Univariate Distributions

Author

Listed:
  • Markos V. Koutras

    (University of Piraeus)

  • Spiros D. Dafnis

    (University of Piraeus)

Abstract

In this work we introduce a wide family of continuous univariate distributions with support $$(0,\infty )$$ ( 0 , ∞ ) that includes as special cases the majority of classical continuous distributions. The new family contains distributions with cumulative distribution function of the form $$F(x;\varvec{\theta })=g^{-1}(h(x;\varvec{\theta }))$$ F ( x ; θ ) = g - 1 ( h ( x ; θ ) ) , where g and h satisfy specific conditions. We study its properties, including aging, tail properties and unimodality, and apply our general results to families of classical distributions, thereof obtaining alternative proofs of well known results. We also discuss how the new framework can be exploited for the generation of new distributions that possess specific desirable properties (e.g. they have heavy tails, monotone failure rates etc).

Suggested Citation

  • Markos V. Koutras & Spiros D. Dafnis, 2025. "A New Family of Continuous Univariate Distributions," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-20, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-024-10131-9
    DOI: 10.1007/s11009-024-10131-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10131-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-024-10131-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    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. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    2. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.
    3. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Matthias Wagener & Andriette Bekker & Mohammad Arashi, 2021. "Mastering the Body and Tail Shape of a Distribution," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    5. Mohsen Maleki & Darren Wraith & Reinaldo B. Arellano-Valle, 2019. "A flexible class of parametric distributions for Bayesian linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 543-564, June.
    6. Peter Neary & Monika MrázováMathieu Parenti, 2015. "Technology, Demand, And The Size Distribution Of Firms," Economics Series Working Papers 774, University of Oxford, Department of Economics.
    7. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Second-order stochastic dominance for decomposable multiparametric families with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 159(C).
    8. Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    9. Sanku Dey & Indranil Ghosh & Devendra Kumar, 2019. "Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data," Annals of Data Science, Springer, vol. 6(4), pages 623-650, December.
    10. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of quantile-based inference in Bayesian models," OSF Preprints enzgs_v1, Center for Open Science.
    11. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Tu, Shiyi & Wang, Min & Sun, Xiaoqian, 2016. "Bayesian analysis of two-piece location–scale models under reference priors with partial information," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 133-144.
    13. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    14. Moreno Bevilacqua & Christian Caamaño-Carrillo & Reinaldo B. Arellano-Valle & Camilo Gómez, 2022. "A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 644-674, September.
    15. Xu, Ganggang & Genton, Marc G., 2015. "Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 78-91.
    16. Jorge Navarro & Jorge M Arevalillo, 2023. "On connections between skewed, weighted and distorted distributions: applications to model extreme value distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1307-1335, December.
    17. Emmanuel O. Ogundimu & Jane L. Hutton, 2016. "A Sample Selection Model with Skew-normal Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 172-190, March.
    18. 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.
    19. Ivanović, Blagoje & Milošević, Bojana & Obradović, Marko, 2020. "Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    20. Simos Meintanis & Bojana Milošević & Marko Obradović, 2023. "Bahadur efficiency for certain goodness-of-fit tests based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 723-751, October.

    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:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-024-10131-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.