normal_quantile

std.stats.normal_quantile · Level L5

The normal distribution's quantile: the x with Φ((x − μ)/σ) = p, as μ + σ·Φ⁻¹(p).

μ + σ·Φ⁻¹(p)

Signature

normal_quantile(p: f64[n], mu: f64[], sigma: 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.

pf64[n]sigmaf64[]muf64[]NdtrizMultiplyszAddqqf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference μ + σ·√2·erfinv(2p − 1) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 177 float64 results inside the running error bound; the closest uses 84% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
48%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
49

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

NOVA computes Φ⁻¹ itself (Acklam's approximation refined by Halley steps). The exact check uses √2·erfinv(2p − 1) at 100 digits, with more digits in deep tails, where 2p − 1 would otherwise round to −1.

Identity

Calls
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Called by
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sha256:b859414fdfbd60b8df28a9502b18bc7e78ed81a126ad208e0171dccc23ec3f99

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