student_t_logpdf

std.stats.student_t_logpdf · Level L5

The log-density of Student's t distribution with ν degrees of freedom: log Γ((ν+1)/2) − log Γ(ν/2) − ½·log(νπ) − ((ν+1)/2)·log1p(x²/ν).

log Γ((ν+1)/2) − log Γ(ν/2) − ½ log(νπ) − (ν+1)/2·log1p(x²/ν)

Signature

student_t_logpdf(x: f64[n], nu: 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]nuf64[]1.00.53.14159Multiplyx2Multiplyh0Addnu1MultiplynupiDividerLogGammalg0Multiplyh1LoglognupiLog1pl1pLogGammalg1MultiplyhlMultiplytailSubtracts1Subtracts2Subtractlogplogpf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference log of Γ((ν+1)/2)/(√(νπ)·Γ(ν/2))·(1 + x²/ν)^(−(ν+1)/2) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 158 float64 results inside the running error bound; the closest uses 12% 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
25%
largest error, in units in the last place
6.27

Identity

Calls
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Called by
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sha256:2d676daf2ecbc2306367f1fdbc513f50484e941dcafbf095458ed1dc295a1564

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