Coherent indexes for shifted count and semicontinuous models

Marcelo Bourguignon () and Célestin C. Kokonendji ()
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Marcelo Bourguignon: Universidade Federal do Rio Grande do Norte
Célestin C. Kokonendji: Université de Franche-Comté

Statistical Papers, 2024, vol. 65, issue 8, No 18, 5253-5271

Abstract: 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.

Keywords: Dispersion index; Inflation index; Multivariate coefficient of variation; Shifted distribution; Mass index; Variation index; 62E10; 62F10; 62H05; 62H12; 62H99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01598-2

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