ABC plots for selected common distributions.

<p>For comparison, the ABC plots for the uniform distribution, <i>U = Uniform [0</i>,<i>m]</i>, where the data points <i>x</i> are drawn with uniform probability </p><p></p><p></p><p></p><p><mn>1</mn></p><p><mi>m</mi></p><p></p><p></p><p></p> within the interval from 0 to a maximum of <i>m</i>, and for the identity distribution i.e., all <i>x</i>_{<b><i>i</i></b>} have the same value <i>x</i>_{<b><i>i</i></b>} = <i>c</i>, are shown as green and magenta lines, respectively. <b>Left upper panel:</b> ABC plot of the Lognormal distribution <i>LN(m</i>,<i>s)</i> with s = 3. The ABC curve for <i>LN(m</i>,<i>s)</i> is independent of <i>m</i>. <b>Upper right panel:</b> ABC plot of the family of exponential distributions with <i>cdf</i> = 1 – <i>e</i>^<i>λx</i>. The ABC curve for these distributions depends on the value of λ. <b>Lower left panel:</b> ABC plot of a Pareto distribution with <p></p><p><mo>=</mo><mn>1</mn><mo>-</mo></p><p></p><p><mo>(</mo></p><p></p><p></p><p></p><p></p><p><mi>x</mi></p><p><mi>m</mi><mi>i</mi><mi>n</mi></p><p></p><p></p><p><mi>x</mi></p><p></p><p></p><mo>)</mo><p></p><p><mi>α</mi></p><p></p><p></p><p></p>. For α = 1.18 the ABC curve passes through the “Pareto” point (see last paragraph of the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129767#sec014" target="_blank">discussion</a>) at 20/80%). <b>Lower right panel:</b> ABC plot of a Gaussian distribution <i>N(5</i>,<i>1)</i>. This distribution shows lower inequality than the uniform distribution (green line) and comes close to the identity distribution (magenta line).<p>