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Tests observed counts against an expected distribution.

public static TestResult GoodnessOfFit(ReadOnlySpan<double> observed, ReadOnlySpan<double> expected = default, NanPolicy nanPolicy = NanPolicy.Propagate)

Parameters — observed are the observed counts, at least one category, one alone leaving no degree of freedom and a NaN p-value as scipy's does; the span is read, never modified. expected are the expected counts, which must sum to the observed total; omit them for a uniform expectation across every category, which is what scipy.stats.chisquare does with f_exp=None. nanPolicy says what to do with a NaN; scipy's nan_policy, defaulting to NanPolicy.Propagate.

Returns — TestResult: the statistic, and the upper-tail p-value.

Exceptions — ArgumentException when there is no category, observed and expected differ in length, an expectation is not positive, or the expectations do not sum to the observations.

Example — six faces of a die, rolled 88 times.

using Lodestar.Stats;

double[] rolls = [16.0, 18.0, 16.0, 14.0, 12.0, 12.0];

TestResult result = ChiSquared.GoodnessOfFit(rolls);

double statistic = result.Statistic;               // => 2
double p = Math.Round(result.PValue, 6);            // => 0.849145

Remarks — a p-value this large says the rolls are entirely consistent with a fair die; the uniform expectation here is 88 / 6 in every category, since expected was omitted. Passing an explicit expected answers a different question — not "is this uniform?" but "does this match this distribution?" — and it must sum to the observed total within 1.49e-8, the square root of the double's machine epsilon, relative to the smaller of the two totals, as scipy's chisquare checks, or the p-value would be comparing tables of different sizes.

Under NanPolicy.Propagate, a NaN or an infinity reaches the statistic. A NaN or an infinite value anywhere in observed drives statistic itself to NaN (an inf - inf, then an inf / inf, inside the loop above), and the p-value follows it rather than throwing the ArgumentOutOfRangeException calling the incomplete gamma function on a NaN would otherwise raise. An infinity with an explicit expected is the exception: the totals then disagree without bound, and the check above refuses it with ArgumentException, as scipy's chisquare raises ValueError. Compare ChiSquared.Contingency, which raises ArgumentException on a NaN cell instead, unchanged by this rule.

Under NanPolicy.Omit the two inputs are filtered together: an index is kept only when neither side holds a NaN, so a pair survives or neither value does.

Applies to — net10.0, netstandard2.0.

See also — ChiSquared.Contingency, FisherExact.Test for a 2×2 table at any sample size, the Python equivalence table.