BETA.DIST Function (LibreOffice Calc)
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.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✔ |
| Libreoffice | ✔ |
| Numbers | ✖ |
| Onlyoffice | ✔ |
| Openoffice | ✖ |
| Wps | ✔ |
| Zoho | ✔ |
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.
Related Patterns and Alternatives ▾
- 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.