BETALN Function (LibreOffice Calc)

• Computes ln(Beta(α, β))
• Provides stable results for large α and β
• Avoids overflow/underflow common in direct beta calculations
• Used in Bayesian modeling, log‑likelihoods, and statistical inference

BETALN(alpha; beta)

Arguments

• alpha:
  Shape parameter α (must be > 0).

• beta:
  Shape parameter β (must be > 0).

Log beta function

=BETALN(2; 5)

Using cell references

=BETALN(A1; B1)

Compare with BETA using exponentiation

=EXP(BETALN(α; β))

Bayesian log‑posterior calculations

=k*LN(p) + (n-k)*LN(1-p) - BETALN(k+1; n-k+1)

Log‑likelihood for binomial‑beta model

=LN(COMBIN(n; k)) + BETALN(k+α; n-k+β) - BETALN(α; β)

Stable computation of beta PDF

=EXP((α-1)*LN(x) + (β-1)*LN(1-x) - BETALN(α; β))

Stable computation of beta-binomial PMF

=EXP(LN(COMBIN(n; k)) + BETALN(k+α; n-k+β) - BETALN(α; β))

Use with GAMMALN identity

=GAMMALN(α) + GAMMALN(β) - GAMMALN(α+β)

BETALN returns a real number (logarithmic value)

Accepts:

• α > 0
• β > 0

Behavior details

• Always returns a finite real number
• More stable than computing LN(BETA())
• Ideal for large α, β, or extreme distributions
• Based on the gamma‑function identity:
  ln(Beta(α, β)) = ln(Γ(α)) + ln(Γ(β)) − ln(Γ(α+β))

Invalid input → Err:502

BETALN of an error → error propagates

• Use BETALN for stable statistical calculations
• Prefer log‑space formulas for large α/β
• Use BETA only for small, well‑behaved parameters
• Combine with GAMMALN for advanced modeling
• Use EXP() only when necessary to convert back to standard scale

• Use BETA for the beta PDF
• Use BETADIST for the cumulative distribution
• Use BETAINV for quantiles
• Use GAMMALN for stable gamma‑function calculations
• Use FACTLN for log‑factorials

By mastering BETALN, you can build robust, numerically stable statistical and Bayesian models in LibreOffice Calc.