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

Célestin C. Kokonendji (), Aboubacar Y. Touré () and Amadou Sawadogo ()
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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

AStA Advances in Statistical Analysis, 2020, vol. 104, issue 2, No 5, 285-307

Abstract: 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.

Keywords: Dependence; Equi-variation; Multivariate dispersion index; Multivariate exponential distribution; Over-variation; Under-variation .; 62E10; 62F10; 62H05; 62H12; 62H99; 62-07 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10182-020-00364-7

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