IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v104y2020i2d10.1007_s10182-020-00364-7.html
   My bibliography  Save this article

Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions

Author

Listed:
  • Célestin C. Kokonendji

    (Université Bourgogne Franche-Comté, UFR Sciences et Techniques)

  • Aboubacar Y. Touré

    (Université Bourgogne Franche-Comté, UFR Sciences et Techniques)

  • Amadou Sawadogo

    (Université Félix Houphouët Boigny)

Abstract

We introduce some new indexes to measure the departure of any multivariate continuous distribution on the nonnegative orthant of the corresponding space from a given reference distribution. The reference distribution may be an uncorrelated exponential model. The proposed multivariate variation indexes that are a continuous analogue to the relative Fisher dispersion indexes of multivariate count models are also scalar quantities, defined as ratios of two quadratic forms of the mean vector to the covariance matrix. They can be used to discriminate between continuous positive distributions. Generalized and multiple marginal variation indexes with and without correlation structure, respectively, and their relative extensions are discussed. The asymptotic behaviors and other properties are studied. Illustrative examples as well as numerical applications are analyzed under several scenarios, leading to appropriate choices of multivariate models. Some concluding remarks and possible extensions are made.

Suggested Citation

  • Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:2:d:10.1007_s10182-020-00364-7
    DOI: 10.1007/s10182-020-00364-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-020-00364-7
    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/s10182-020-00364-7?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. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    2. Abid, Rahma & Kokonendji, Célestin C. & Masmoudi, Afif, 2019. "Geometric dispersion models with real quadratic v-functions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 197-204.
    3. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    4. Johann Cuenin & Bent Jørgensen & Célestin C. Kokonendji, 2016. "Simulations of full multivariate Tweedie with flexible dependence structure," Computational Statistics, Springer, vol. 31(4), pages 1477-1492, December.
    5. Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.
    6. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    7. Wagner Hugo Bonat & Bent Jørgensen, 2016. "Multivariate covariance generalized linear models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 649-675, November.
    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. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.

    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. Marcelo Bourguignon & Célestin C. Kokonendji, 2024. "Coherent indexes for shifted count and semicontinuous models," Statistical Papers, Springer, vol. 65(8), pages 5253-5271, October.
    2. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.
    3. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    4. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    5. Célestin C. Kokonendji & Aboubacar Y. Touré & Rahma Abid, 2022. "On General Exponential Weight Functions and Variation Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 924-940, August.
    6. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    7. Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.
    8. W. H. Bonat & J. Olivero & M. Grande-Vega & M. A. Farfán & J. E. Fa, 2017. "Modelling the Covariance Structure in Marginal Multivariate Count Models: Hunting in Bioko Island," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 446-464, December.
    9. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
    10. Maria Victoria Ibañez & Marina Martínez-Garcia & Amelia Simó, 2021. "A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data," Mathematics, MDPI, vol. 9(13), pages 1-23, July.
    11. Indranil Ghosh, 2023. "A New Class of Alternative Bivariate Kumaraswamy-Type Models: Properties and Applications," Stats, MDPI, vol. 6(1), pages 1-21, January.
    12. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    13. Arnold Barry C. & Arvanitis Matthew, 2021. "On a general class of gamma based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 374-384, January.
    14. 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.
    15. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    16. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    17. Soltani, Ali & Roohani Qadikolaei, Mohsen, 2024. "Space-time analysis of accident frequency and the role of built environment in mitigation," Transport Policy, Elsevier, vol. 150(C), pages 189-205.
    18. Catalina Bolancé & Montserrat Guillen & Albert Pitarque, 2020. "A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    19. Nozer D. Singpurwalla & Barry C. Arnold & Joseph L. Gastwirth & Anna S. Gordon & Hon Keung Tony Ng, 2016. "Adversarial and Amiable Inference in Medical Diagnosis, Reliability and Survival Analysis," International Statistical Review, International Statistical Institute, vol. 84(3), pages 390-412, December.

    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:alstar:v:104:y:2020:i:2:d:10.1007_s10182-020-00364-7. 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.