gamma_logpdf

std.stats.gamma_logpdf · Level L5

The log-density of the gamma distribution with shape a and rate b: a·log b + (a − 1)·log x − b·x − log Γ(a).

a·log b + (a−1)·log x − b·x − log Γ(a)

Signature

gamma_logpdf(x: f64[n], shape: f64[], rate: 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.

xf64[n]ratef64[]1.0shapef64[]MultiplybxLoglogxSubtractam1LoglogbLogGammalgaMultiplyt2Multiplyt1Adds1Subtracts2Subtractlogplogpf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference log(bᵃ·xᵃ⁻¹·e^(−bx) / Γ(a)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 143 float64 results inside the running error bound; the closest uses 21% 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
27%
largest error, in units in the last place
31

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.

Note

The reference forms the density itself, with Γ rather than log Γ, then takes its logarithm: a different route to the same value.

Identity

Calls
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Called by
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sha256:ac8c05fc5b845dd3f7487f88344d894b1eae352d8e06fdec1d6a15d0237c070b

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