beta_cdf

std.stats.beta_cdf · Level L5

The beta distribution's cumulative probability: I_x(a, b), the regularized incomplete beta function.

F(x; a, b) = I_x(a, b)

Signature

beta_cdf(x: f64[n], a: f64[], b: 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 scipy.special.betainc(a, b, x) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 122 float64 results inside the running error bound; the closest uses 7% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 27%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 39

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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sha256:6c3bb29edd6013b920bdb3b110692ae3e7236712c657f86f3aa44c0307fa254c

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.beta_cdf · Ω:beta_cdf
Pins: sha256:283e75fdd36953f69a345039674b455605b5bab101cb695fd9cb49e053f28f75this graph alone
Evidence: sha256:4808b12ac20dcef77f4df424738394f1b6ae993efe6b729efb081d54b96decd9the 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.