Poverty & Inequality Explorer grouped data · Lorenz curves · FGT · Datt–Ravallion
Most published distribution data is grouped: ten decile shares and a mean rather than a microdata file. This page does what POVCAL did with such data. It fits parametric Lorenz curves (General Quadratic and Beta), recovers the whole quantile function, and from that computes Gini, Theil, mean log deviation, Atkinson, the Palma ratio and the Foster–Greer–Thorbecke poverty measures at any line; between two surveys it decomposes the change in poverty into growth and redistribution and draws the growth incidence curve. Decile data can be pulled live from the World Bank's Poverty and Inequality Platform, or typed in.
Distribution
Means and lines are per person per day in 2021 PPP dollars; deciles are shares of total welfare. Source rows are national, urban or rural, consumption or income, as PIP labels them.
Poverty line
The three presets are the World Bank's global lines adopted in June 2025 in 2021 PPP dollars, replacing $2.15, $3.65 and $6.85 in 2017 PPP.
Lorenz curve
Choose a distribution to begin.
Inequality
How these are computed
Every measure is computed from the fitted quantile function y(p) = μ·L′(p) on a grid of 4,000 population points, so the numbers are those of the fitted curve rather than of the ten points. Gini = 1 − 2∫L(p)dp. Theil T = ∫(y/μ)ln(y/μ)dp; mean log deviation = ∫ln(μ/y)dp; Atkinson(ε) = 1 − [∫(y/μ)1−εdp]1/(1−ε), with the geometric-mean form at ε = 1. The Palma ratio is the top 10% share over the bottom 40% share, read off the fitted curve. The “from the points” Gini is the trapezoid on the raw cumulative shares, which is always a lower bound because it assumes equality within each decile.
Poverty
How these are computed
The headcount H is the p at which the fitted quantile y(p) crosses the line z, found by bisection. FGTα = ∫0H(1 − y(p)/z)αdp: α = 0 is the headcount, α = 1 the poverty gap (mean shortfall as a share of the line, over the whole population), α = 2 the squared gap that weights the poorest most. Watts = ∫0H ln(z/y)dp. The sensitivity curve re-solves H for a range of lines; a steep curve near the chosen line means the headcount is fragile to where the line is drawn.
Change between surveys Datt–Ravallion
How these are computed
With P(μ, L) the poverty measure implied by mean μ and Lorenz curve L, the change from A to B is split into a growth component P(μB, LA) − P(μA, LA), a redistribution component P(μA, LB) − P(μA, LA) and a residual (Datt and Ravallion 1992). The Shapley version averages each component over both reference points so the residual vanishes (Shorrocks 1999; Kolenikov and Shorrocks 2005). The growth incidence curve (Ravallion and Chen 2003) is the growth in y(p) between the two fitted quantile functions at each percentile; when it lies above the mean growth for low p, growth was pro-poor in the relative sense.