Calculate Atkinson Index of Health Inequality — calc_atkinson

The Atkinson index measures the extent of inequality in the health distribution, explicitly incorporating a parameter \(\varepsilon\) representing inequality aversion. Higher \(\varepsilon\) values give more weight to health differences at the bottom of the distribution.

Usage

calc_atkinson_index(health_dist, pop_weights, epsilon = 1)

Arguments

health_dist: Numeric vector of health values across population groups.
pop_weights: Numeric vector of population weights (need not sum to 1; will be normalised internally).
epsilon: Inequality aversion parameter (default = 1). Must be non-negative. When \(\varepsilon = 0\), returns 0 (no aversion).

Value

Atkinson index value in [0, 1]. A value of 0 indicates perfect equality; a value approaching 1 indicates maximum inequality.

References

Atkinson AB (1970). On the Measurement of Inequality. Journal of Economic Theory 2(3): 244-263. doi:10.1016/0022-0531(70)90039-6

Examples

# Perfect equality
calc_atkinson_index(rep(70, 5), rep(0.2, 5), epsilon = 1)
#> [1] -4.440892e-16

# Gradient across groups
calc_atkinson_index(c(60, 63, 66, 69, 72), rep(0.2, 5), epsilon = 1)
#> [1] 0.002071263