bcsdistance function

Calculates the blended Chi-square distance matrix between n vectors

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.

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.

Returns

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