f_cdf

std.stats.f_cdf · Level L5

The F distribution's cumulative probability with d₁ and d₂ degrees of freedom: I_{d₁x/(d₁x+d₂)}(d₁/2, d₂/2), the regularized incomplete beta function.

F(x) = I_{d₁x/(d₁x+d₂)}(d₁/2, d₂/2)

Signature

f_cdf(x: f64[n], d1: f64[], d2: f64[]) → 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 betainc(d1/2, d2/2, d1·x/(d1·x + d2)) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 149 float64 results inside the running error bound; the closest uses 37% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 40% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 15%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 2.5e+4

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

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Called by

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sha256:8f56d02ddaab21dcf0a1776d445096376ee70e7c0e9ee86de020fc70d2408565

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.f_cdf · Ω:f_cdf
Pins: sha256:343d6f0710032af0940bb793e12def1a512cc421224115f6c38506a8d79ae8f5this graph alone
Evidence: sha256:07a3e212ca9b040f779d015115bb7a26d370c207143b72b74b5110ad2b150f2fthe 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.