poisson_logpmf

std.stats.poisson_logpmf · Level L5

The log-probability of k events under a Poisson distribution with mean λ: k·log λ − λ − log k!, with log k! as log Γ(k + 1).

log P(k) = k·log λ − λ − log Γ(k + 1)

Signature

poisson_logpmf(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]lamf64[n]1LogloglamAddk1MultiplyklogLogGammalogfactSubtracttSubtractlogplogpf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference k·log λ − λ − log(k!), with the exact factorial to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 175 float64 results inside the running error bound; the closest uses 9% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
59%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
7.07

Identity

Calls
—
Called by
—
sha256:1b0f34db14a5492cdebb076fd18aa237866bd7e61ab6a9341dcff14b2f01fe01

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