BL {wINEQ}

Blair and Lacy index

Description

Computes Blair and Lacy inequality measure of a given variable taking into account weights.

Usage

BL(X, W = rep(1, length(X)), withsqrt = FALSE)

Arguments

X

is a data vector (numeric or ordered factor)

W

is a vector of weights

withsqrt

if TRUE function returns index given by BL2, elsewhere by BL (default). See more in details.

Details

Let m be the median category, n be the number of categories and P_i be the cumulative distribution of i-th category. The indices of Blair and Lacy (2000) are the following:

BL = 1-\frac{\sum_{i=1}^{n-1}(P_{i}-0.5)^2}{\frac{n-1}{4}}

BL2 = 1-\left(\frac{\sum_{i=1}^{n-1}(P_{i}-0.5)^2}{\frac{n-1}{4}}\right)^{\frac{1}{2}}

Value

The value of Blair and Lacy coefficient.

References

Blair J, Lacy M G. (2000): Statistics of ordinal variation, Sociological Methods and Research 28(251);251-280.

Examples

# Compare weighted and unweighted result
X=1:10
W=1:10
BL(X)
BL(X,W)

data(Well_being)
# Blair and Lacy index for health assessment with sample weights
X=Well_being$V1
W=Well_being$Weight
BL(X,W)