import mir.math.common: approxEqual, pow;
import mir.math.sum: Summation;
import mir.ndslice.slice: sliced;

auto x = [0.0, 1.0, 1.5, 2.0, 3.5, 4.25,
          2.0, 7.5, 5.0, 1.0, 1.5, 0.0].sliced;

SkewnessAccumulator!(double, SkewnessAlgo.online, Summation.naive) v;
v.put(x);
assert(v.skewness(true).approxEqual((117.005859 / 12) / pow(54.765625 / 12, 1.5)));
assert(v.skewness(false).approxEqual((117.005859 / 12) / pow(54.765625 / 11, 1.5) * (12.0 ^^ 2) / (11.0 * 10.0)));

v.put(4.0);
assert(v.skewness(true).approxEqual((100.238166 / 13) / pow(57.019231 / 13, 1.5)));
assert(v.skewness(false).approxEqual((100.238166 / 13) / pow(57.019231 / 12, 1.5) * (13.0 ^^ 2) / (12.0 * 11.0)));