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Fisher dispersion index for multivariate count distributions: A review and a new proposal

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  • Kokonendji, Célestin C.
  • Puig, Pedro

Abstract

The Fisher dispersion index is very widely used to measure the departure of any univariate count distribution from the equidispersed Poisson model. A multivariate extension has not yet been well defined and discussed in the literature. In this paper, a new definition of the multivariate Fisher index through the generalized dispersion index is proposed. This is a scalar quantity, defined as a ratio of two quadratic forms of the mean vector and the covariance matrix. A multiple marginal dispersion index and its relative extension for a given reference count distribution are discussed, and the asymptotic behavior and other properties are studied. Illustrative examples and practical applications on count datasets are analyzed under several scenarios. Some concluding remarks are made, including challenging problems.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:180-193
    DOI: 10.1016/j.jmva.2017.12.010
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    1. 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.
    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, 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. 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.
    5. 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.

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