| bcsdistance {smacofx} | R Documentation |
Calculates the blended Chi-square distance matrix between n vectors
Description
The pairwise blended chi-distance of two vectors x and y is sqrt(sum(((x[i]-y[i])^2)/(2*(ax[i]+by[i])))), with originally a in [0,1] and b=1-a as in Lindsay (1994) (but we allow any non-negative a and b). The function calculates this for all pairs of rows of a matrix or data frame x.
Usage
bcsdistance(x, a = 0.5, b = 1 - a)
Arguments
x |
an n times p numeric matrix or data frame. Note that the valeus of x must be non-negative. |
a |
first blending weight. Must be non-negative and should be in [0,1] if a blended chi-square distance as in Lindsay (1994) is sought. Defaults to 0.5. |
b |
second blending weight. Must be non-negative and should be 1-a if a blended chi-square distance as in Lindsay (1994) is sought. Defaults to 1-a. |
Value
a symmetric n times n matrix of pairwise blended chi-square distance (between rows of x) with 0 in the main diagonal. It is an object of class distance and matrix with attributes "method", "type" and "par", the latter returning the a and b values.
References
Lindsay (1994). Efficiency versus robustness: the case for minimum Hellinger distance and related methods. Annals of Statistics, 22 (2), 1081-1114. <doi:10.1214/aos/1176325512>