sketch_moments.nx

sketch_moments.nx -- streaming higher moments (skewness + kurtosis). Extends sketch_stream_stats with 3rd and 4th central moments via a naive cumulative-power approach: sum_x = Σ x_i sum_x2 = Σ x_i² sum_x3 = Σ x_i³ sum_x4 = Σ x_i⁴ From these, central moments via the algebraic identities: mean = sum_x / n var = sum_x2/n - mean² m3 = sum_x3/n - 3·mean·var - mean³ (third central) m4 = sum_x4/n - 4·mean·(sum_x3/n) + 6·mean²·(sum_x2/n) - 3·mean⁴ skewness = m3 / σ³ (Fisher-Pearson) kurtosis = m4 / σ⁴ - 3 (excess kurtosis; normal distribution = 0) OVERFLOW BUDGET (CRITICAL): sum_x4 grows like n · |x|⁴. For |x| up to 2^16 and n up to 2^30, sum_x4 < 2^30 · 2^64 → overflows i64 (which caps at 2^63). Tight bound: n · |x|⁴ < 2^62. E.g. |x| <= 2^11 (~2K) and n <= 2^18 (~260K) are safe. Caller responsibility. nx_mom_safe_p flags unsafe values. FOR PROPER OBSERVABILITY ENGINEERING: use this with normalized / quantized inputs (e.g. milliseconds with values < 2K, sample counts < 100K). For broader ranges, use sketch_reservoir + caller-side computation on the sample. LOSSLESS-LANGUAGE DISCIPLINE: skewness/kurtosis envelope is NX_ENV_REL_STDDEV with param_a ~ 1/sqrt(n) (standard error of higher-moment estimators). Caller treats these as bounded-error statistics over the integer-exact accumulators.