ICGE (version 0.4.2)

dbhatta: Bhattacharyya Distance

Description

dbhatta computes and returns the Bhattacharyya distance matrix between the rows of a data matrix. This distance is defined between two units \(i=(p_{i1},...,p_{im})\) and \(j=(p_{j1},...,p_{jm})\) being \(p_{kl}\) frequencies with \(p_{kl}>=0\) and \(p_{k1}+...+p_{km}=1\).

Usage

dbhatta(x)

Value

A dist object with distance information.

Arguments

x

a matrix containing, in its rows, the frequencies for each unit. Note: check that each row adds up to 1

Author

Itziar Irigoien ; Konputazio Zientziak eta Adimen Artifiziala, Euskal Herriko Unibertsitatea (UPV-EHU), Donostia, Spain.

Conchita Arenas ; Departament d'Estadistica, Universitat de Barcelona, Barcelona, Spain.

References

Bhattacharyya, A. (1946). On a measure of divergence of two multinomial populations. Sankhya: The Indian Journal of Statistics, Series A. 14, 177-136.

See Also

dist, dmahal, dgower, dcor, dproc2

Examples

#5 individuals represented by their relative frequencies of 4 characteristics (M1-M4):
f <- matrix(c(0.36, 0.21, 0.23, 0.20,
              0.66, 0.18, 0.11, 0.05,
              0.01, 0.24, 0.62, 0.13,
              0.43, 0.38, 0.08, 0.11,
              0.16, 0.07, 0.09, 0.68), 
              byrow=TRUE, nrow=5, dimnames=list(1:5, paste("M", 1:4, sep="")))

# Bhattacharyya distances between pairs 
d <- dbhatta(f)