binomial_cdf

std.stats.binomial_cdf · Level L5

The probability of at most k successes in k + m independent trials with success probability p (m ≥ 1): I_{1−p}(m, k + 1).

P(K ≤ k) = I_{1−p}(m, k + 1), n = k + m

Signature

binomial_cdf(k: i64[n], m: i64[n], prob: f64[n]) → 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.

mi64[n]ki64[n]1probf64[n]1.0Addk1SubtractqBetaIncppf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference Σ_{j≤k} C(n, j)·pʲ·(1 − p)ⁿ⁻ʲ, summed directly to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 162 float64 results inside the running error bound; the closest uses 1% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
31%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
114

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
—
Called by
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sha256:7fcb4b17d03f602bf5d713be23772a9994e4a0c07a3faef175c350ae7e081a37

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.binomial_cdf · Ω:binomial_cdf
Pins
sha256:ba43df9275f6ba50a097c4d905a36c81aabe27aca3db0ee2c3d40e19c7db7eeethis graph alone
Evidence
sha256:b3bfd1ca0590d20a4e9b239992cbf3d1200117a7d53fa9f28e249b37bb568ee7the 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.