BETA Function (LibreOffice Calc)

• Computes the beta probability density function (PDF)
• Supports optional lower/upper bounds
• Models continuous variables constrained to a finite interval
• Used in Bayesian priors/posteriors, A/B testing, and reliability

Standard form (0 to 1)

BETA(x; alpha; beta)

Bounded form (a to b)

BETA(x; alpha; beta; a; b)

Arguments

• x:
  Value at which to evaluate the density.

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

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

• a (optional):
  Lower bound of the interval (default = 0).

• b (optional):
  Upper bound of the interval (default = 1).

Standard beta PDF

=BETA(0.5; 2; 5)

Bounded beta PDF

=BETA(7; 3; 4; 0; 10)

Using cell references

=BETA(A1; B1; C1)

Bayesian posterior density

=BETA(p; Successes+1; Failures+1)

A/B testing: density at observed conversion rate

=BETA(A1; A2+1; A3+1)

Reliability modeling (bounded variable)

=BETA(A1; 3; 4; 10; 20)

Normalize x for bounded beta

=BETA((A1 - a) / (b - a); α; β)

Compute log‑density for numerical stability

=EXP(LN(BETA(x; α; β)))

Use with BETADIST for full distribution analysis

=BETADIST(x; α; β)   (CDF)  
=BETA(x; α; β)       (PDF)

BETA returns a numeric density value (not a probability)

Accepts:

• x within [a, b]
• α > 0
• β > 0

Behavior details

• If x < a or x > b → returns 0
• Density can exceed 1 (PDFs are not probabilities)
• α and β control skewness and shape
• Default bounds are 0 and 1
• Sensitive to extreme α/β values

Invalid input → Err:502

BETA of an error → error propagates

• Use BETA for density modeling and Bayesian posterior shapes
• Use BETADIST for cumulative probabilities
• Validate α and β to avoid domain errors
• Use bounded form for real‑world ranges
• Combine with BETAINV for quantile analysis

• Use BETADIST for cumulative distribution
• Use BETAINV for inverse cumulative distribution
• Use GAMMALN for stable parameter calculations
• Use NORMDIST, FDIST, and GAMMADIST for other distributions

By mastering BETA, you can build powerful statistical, Bayesian, and probability‑driven models in LibreOffice Calc.