poisson_cdf

std.stats.poisson_cdf · Level L5

The probability of at most k events under a Poisson distribution with mean λ: 1 − P(k + 1, λ).

P(K ≤ k) = 1 − P(k + 1, λ)

Signature

poisson_cdf(k: i64[n], lam: 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference e^(−λ)·Σ_{j≤k} λʲ/j!, summed directly to 80 digits (100-digit arithmetic), on all 40 test cases.
All 131 float64 results inside the running error bound; the closest uses 48% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 90%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 5.14

Identity

Calls

—

Called by

—

sha256:517e07af8ece991da3686a0e12996dd95af475eca32e07a0109c3c8bb09ae770

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.poisson_cdf · Ω:poisson_cdf
Pins: sha256:24289b9f4a5550b18e8395ac3d7bb794aa989bfe582618a430baf66f23f9c0fethis graph alone
Evidence: sha256:07fc69afed576f0732f22108b62b28ddd919e4a644b82e967cbaccc5661091b0the 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.