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BETA.DIST Function (LibreOffice Calc)

Statistical Advanced LibreOffice Calc LibreOffice 4.0

The BETA.DIST function returns either the probability density function (PDF) or cumulative distribution function (CDF) of the beta distribution. It is used in Bayesian inference, A/B testing, reliability modeling, and bounded probability analysis.

The **BETA.DIST** function returns either the **PDF** (probability density) or **CDF** (cumulative probability) of the beta distribution. It is widely used in Bayesian inference, A/B testing, reliability engineering, and modeling continuous variables on bounded intervals.

What the BETA.DIST Function Does

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

Syntax

Standard form (0 to 1)

BETA.DIST(x; alpha; beta; cumulative)

Bounded form (a to b)

BETA.DIST(x; alpha; beta; cumulative; a; b)

Arguments

  • x:
    Value at which to evaluate the distribution.

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

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

  • cumulative:
    TRUE → CDF
    FALSE → PDF

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

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

Basic Examples

Standard beta PDF

=BETA.DIST(0.5; 2; 5; FALSE)

Standard beta CDF

=BETA.DIST(0.5; 2; 5; TRUE)

Bounded beta PDF

=BETA.DIST(7; 3; 4; FALSE; 0; 10)

Using cell references

=BETA.DIST(A1; B1; C1; D1)

Advanced Examples

Bayesian posterior CDF

=BETA.DIST(p; Successes+1; Failures+1; TRUE)

A/B testing: probability conversion rate ≤ x

=BETA.DIST(x; A_success+1; A_fail+1; TRUE)

Reliability modeling (bounded variable)

=BETA.DIST(A1; 3; 4; TRUE; 10; 20)

Compute central credible interval

=BETA.DIST(x; α; β; TRUE)

Convert bounded variable to 0–1 scale

=BETA.DIST((x-a)/(b-a); α; β; TRUE)

Validate PDF/CDF relationship

=BETA.DIST(x; α; β; FALSE)
=BETA.DIST(x; α; β; TRUE)

Edge Cases and Behavior Details

BETA.DIST returns a numeric value

  • PDF → density (may exceed 1)
  • CDF → probability (0–1)

Accepts:

  • x within [a, b]
  • α > 0
  • β > 0

Behavior details

  • If x < a or x > b → returns 0
  • PDF is not a probability; it can exceed 1
  • CDF is always non‑decreasing
  • Bounded form rescales x to [0,1] internally
  • Sensitive to extreme α/β values

Invalid input → Err:502

BETA.DIST of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • α ≤ 0 or β ≤ 0
  • a ≥ b
  • x outside bounds
  • Non-numeric input

Fix:

  • Validate α and β
  • Ensure a < b
  • Clamp x to valid range

Confusing PDF with CDF

Cause:

  • cumulative flag set incorrectly

Fix:

  • TRUE → CDF
  • FALSE → PDF

Best Practices

  • Use PDF for density modeling
  • Use CDF 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 BETALN for stable log‑space calculations
BETA.DIST is the workhorse for Bayesian inference, A/B testing, and any workflow requiring the shape or cumulative behavior of a bounded probability distribution.
  • Use BETA for the PDF only
  • Use BETAINV for inverse cumulative distribution
  • Use BETALN for stable log‑beta calculations
  • Use GAMMALN for stable gamma‑function calculations
  • Use NORM.DIST, F.DIST, and GAMMA.DIST for other distributions

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