beta_cdf

std.stats.beta_cdf · Level L5

The beta distribution's cumulative probability: I_x(a, b), the regularized incomplete beta function.

F(x; a, b) = I_x(a, b)

Signature

beta_cdf(x: f64[n], a: f64[], b: 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]af64[]bf64[]BetaIncppf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference scipy.special.betainc(a, b, x) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 122 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)
27%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
39

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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sha256:6c3bb29edd6013b920bdb3b110692ae3e7236712c657f86f3aa44c0307fa254c

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