migration.gini.exchange {migration.indices}

Exchange Gini Index

Description

The Exchange Gini Index "indicates the contribution to spatial focusing represented by the n(n-q) net interchanges in the system":

G^T_{RC, CR} = \frac{\sum_i \sum_{j \neq i} | M_{ij} - M_{ji} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}

This implementation solves the above formula by simply substracting the transposed matrix's values from the original one at one go.

Usage

migration.gini.exchange(m)

Arguments

m

migration matrix

Value

A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.

References

• David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262

See Also

migration.gini migration.gini.exchange.standardized

Examples

data(migration.hyp)
migration.gini.exchange(migration.hyp)     # 0.05555556
migration.gini.exchange(migration.hyp2)    # 0.04166667