Autore
Sebastiani, Maria Rita

Titolo
A Variability index for spatial series of rates
Periodico
Università degli Studi di Roma "La Sapienza" - Dipartimento di Studi Geoeconomici, Linguistici, Statistici e Storici per l'Analisi regionale. Working papers
Anno: 2007 - Fascicolo: 41 - Pagina iniziale: 1 - Pagina finale: 19

In this paper we introduce a new normalized index for studying the variability of rates measured at various sites. We define a suitable absolute index and, then, in aim to apply a normalization procedure, we investigate the minimum and maximum of the absolute index. The problem of determining the minimum and maximum of a variability index has been studied widely in the literature for statistical distributions of non-negative variables. Existing solutions, however, cannot be directly applied to series of rates, especially those that take values between 0 and 1, such as birth or death rates. Indeed, if the rates comply with some logical or formal constraints, the series of rates with minimum or maximum variability must comply with the same constraints. Here, we consider rates where the variable X in the numerator is non-negative and such that the total of X values over all spatial units can be transferred partly or totally amongst units. We implement an algorithm in R for determining analytically the minimum and maximum of the absolute index for a given series and the corresponding value of the normalized index. We use the proposed methodology for evaluating if European populations converge across time towards a common demographical profile. In this aim, we apply the normalized index to several series, each corresponding to a given demographical rate (crude birth rate, crude death rate and infant mortality rate) and to a specific framework of the European Union (specifically, with 6, 10, 12, 15, 25 and 27 member countries), for every year from 1960 to 2004.




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