BL {wINEQ}R Documentation

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 mm be the median category, nn be the number of categories and PiP_i be the cumulative distribution of ii-th category. The indices of Blair and Lacy (2000) are the following:

BL=1i=1n1(Pi0.5)2n14BL = 1-\frac{\sum_{i=1}^{n-1}(P_{i}-0.5)^2}{\frac{n-1}{4}}

BL2=1(i=1n1(Pi0.5)2n14)12BL2 = 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)



[Package wINEQ version 1.2.0 Index]