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

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  • 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
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    References listed on IDEAS

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    1. Bent Jørgensen & Célestin Kokonendji, 2016. "Discrete dispersion models and their Tweedie asymptotics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 43-78, January.
    2. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

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