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Coherent indexes for shifted count and semicontinuous models

Author

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  • Marcelo Bourguignon

    (Universidade Federal do Rio Grande do Norte)

  • Célestin C. Kokonendji

    (Université de Franche-Comté)

Abstract

Nonnegative distributions display certain specific indexes such as dispersion and inflation for count models as well as recent variation and mass indexes for semicontinuous ones. When the support of the model is, for instance, shifted from zero, then several authors use the original indexes with respect to the inappropriate reference model. The current paper elaborates coherent indexes for shifted count and semicontinuous models in order to measure the departure of a suitable reference distribution. From this perspective, we start from the usual reference distributions which are uncorrelated shifted Poisson and uncorrelated shifted exponential models. Concerning the corresponding variability indexes, multiple marginal ones and novel multivariate coefficients of variation are thus deduced. Owing to their relativities, all these indexes can be used to discriminate between two comparable distributions and, also, within a given model. Empirical indexes are, therefore, considered with some asymptotic properties. Useful univariate one-count models are examined in terms of dispersion and inflation indexes. In addition, some univariate shifted semicontinuous models are mainly illustrated for variation index. Finally, an application to count data is enacted and pertinent concluding remarks are drawn such the limitations and future work points.

Suggested Citation

  • Marcelo Bourguignon & Célestin C. Kokonendji, 2024. "Coherent indexes for shifted count and semicontinuous models," Statistical Papers, Springer, vol. 65(8), pages 5253-5271, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01598-2
    DOI: 10.1007/s00362-024-01598-2
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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. 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.
    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. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    5. 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.
    6. 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.
    7. Aboubacar Y. Touré & Simplice Dossou-Gbété & Célestin C. Kokonendji, 2020. "Asymptotic normality of the test statistics for the unified relative dispersion and relative variation indexes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2479-2491, November.
    8. 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.
    9. Youssef Esstafa & Célestin C. Kokonendji & Sobom M. Somé, 2023. "Asymptotic properties of the normalised discrete associated-kernel estimator for probability mass function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(2), pages 355-372, April.
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