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.

ki64[n]1lamf64[n]Addk1GammaInclower1.0Subtractppf64[n]
  • 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
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Called by
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sha256:517e07af8ece991da3686a0e12996dd95af475eca32e07a0109c3c8bb09ae770

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