chi2_sf

std.stats.chi2_sf · Level L5

The chi-square distribution's upper tail with k degrees of freedom, the p-value of a chi-square statistic: Q(k/2, x/2), the regularized upper incomplete gamma function. A small p-value keeps its relative accuracy, where 1 − chi2_cdf would round it to 0.

P(X > x; k) = Q(k/2, x/2)

Signature

chi2_sf(x: f64[n], k: i64[]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference closed forms for whole k: e^(−x/2)·Σ…, or erfc(√(x/2)) + …, summed directly to 80 digits (100-digit arithmetic), on all 40 test cases.
All 143 float64 results inside the running error bound; the closest uses 6% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 81%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 9.03

Note

For whole degrees of freedom the upper tail has closed forms that are sums of positive terms, so the reference never subtracts from 1.

Identity

Calls

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Called by

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sha256:061156f5666d5d03d6e987874b5510b161d3b411966fd84a1a5cd0a54ad5b9be

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.chi2_sf · Ω:chi2_sf
Pins: sha256:3af7cb1868121b6681b0c1afce102dab30adf3d5e76b7a01fa513ab5efc425d6this graph alone
Evidence: sha256:7e1994126121a21a22d4198f4d53ef7a601bb21b61cc5d3425f0384665c4c5d3the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.