wINEQ (version 1.2.1)

BL: 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)

Value

The value of Blair and Lacy coefficient.

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

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)