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@ac-kit

logBeta

logBeta(a, b): number

Defined in: packages/math-analysis/src/log-beta.ts:31

The natural logarithm of the beta function, ln B(a, b).

The form to use once the shapes get large: B(a, b) underflows to zero from around a + b ≈ 1500, and this keeps full relative precision well past that. It is also what you want any time the result was going to be logged, summed with other logs, or exponentiated at the end — which is most of what a likelihood calculation does.

Not a wrapper around Math.log(beta(a, b)): below the underflow point that is exactly what it computes, because the log of an accurate value carries only its own rounding, and above it a sum of three log-gammas takes over.

O(1) time, O(1) memory.

Parameters

Section titled “Parameters”

a

Section titled “a”

number

First shape parameter, positive.

b

Section titled “b”

number

Second shape parameter, positive.

Returns

Section titled “Returns”

number

ln B(a, b), or NaN when either parameter is non-positive.

Example

Section titled “Example”
  logBeta(500, 500); // -694.9887224857135
  logBeta(2000, 2000); // -2775.1235988460758 — where beta() returns 0
  ```;


## See


 - [beta](beta.md) for the value itself.
 - [The gamma and beta functions](https://anthochamp.pages.grenadine.io/node-essentials/topics/math/functions/gamma/)