gamma_cdf

std.stats.gamma_cdf · Level L5

The gamma distribution's cumulative probability with shape a and rate b: P(a, b·x).

F(x; a, b) = P(a, b·x)

Signature

gamma_cdf(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[]shapef64[]MultiplytGammaIncppf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference scipy.special.gammainc(a, b·x) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 154 float64 results inside the running error bound; the closest uses 14% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
47%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
16

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
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Called by
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sha256:9aa3479c9766840949f259af79dda0a36da84ec1130ce86c5cc69f988d528987

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