BETA.INV Function (LibreOffice Calc)
The BETA.INV function returns the inverse of the cumulative beta distribution (quantile function). It is used in Bayesian inference, A/B testing, reliability modeling, and determining percentiles of bounded probability distributions.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✔ |
| Libreoffice | ✔ |
| Numbers | ✖ |
| Onlyoffice | ✔ |
| Openoffice | ✖ |
| Wps | ✔ |
| Zoho | ✔ |
What the BETA.INV Function Does ▾
- Computes the quantile of the beta distribution
- Solves for x such that CDF(x) = probability
- Supports optional lower/upper bounds
- Used in Bayesian credible intervals, A/B testing, and reliability
Syntax ▾
Standard form (0 to 1)
BETA.INV(probability; alpha; beta)
Bounded form (a to b)
BETA.INV(probability; alpha; beta; a; b)
Arguments
-
probability:
Cumulative probability (0–1). -
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).
Basic Examples ▾
50th percentile (median) of a beta distribution
=BETA.INV(0.5; 2; 5)
95th percentile
=BETA.INV(0.95; 2; 5)
Bounded beta quantile
=BETA.INV(0.9; 3; 4; 0; 10)
Using cell references
=BETA.INV(A1; B1; C1)
Advanced Examples ▾
Bayesian credible interval (lower bound)
=BETA.INV(0.025; Successes+1; Failures+1)
Bayesian credible interval (upper bound)
=BETA.INV(0.975; Successes+1; Failures+1)
A/B testing: 90% quantile of conversion rate
=BETA.INV(0.9; A_success+1; A_fail+1)
Reliability modeling (bounded variable)
=BETA.INV(0.95; 3; 4; 10; 20)
Validate inversion
=BETA.DIST(BETA.INV(p; α; β); α; β; TRUE)
Convert bounded quantile to 0–1 scale
=BETA.INV(p; α; β; a; b)
Edge Cases and Behavior Details ▾
BETA.INV returns a value x within [a, b]
Accepts:
- 0 ≤ probability ≤ 1
- α > 0
- β > 0
Behavior details
- If probability = 0 → returns a
- If probability = 1 → returns b
- Quantile is monotonic increasing
- Bounded form rescales internally
- Sensitive to extreme α/β values
Invalid input → Err:502
BETA.INV of an error → error propagates
Common Errors and Fixes ▾
Err:502 — Invalid argument
Cause:
- α ≤ 0 or β ≤ 0
- probability outside 0–1
- a ≥ b
- Non-numeric input
Fix:
- Validate α and β
- Clamp probability to [0,1]
- Ensure a < b
Unexpected extreme values
Cause:
- Highly skewed distributions
- α or β very small
Fix:
- Inspect distribution shape
- Use BETALN for stable log‑space modeling
Best Practices ▾
- Use BETA.INV for quantiles and credible intervals
- Use BETA.DIST for PDF/CDF
- Validate α and β to avoid domain errors
- Use bounded form for real‑world ranges
- Combine with BETALN for stable log‑likelihoods
BETA.INV is essential for Bayesian credible intervals, A/B testing thresholds, and any workflow requiring percentiles of a bounded probability distribution.
Related Patterns and Alternatives ▾
- Use BETA.DIST for PDF/CDF
- Use BETALN for stable log‑beta calculations
- Use GAMMALN for stable gamma‑function calculations
- Use NORM.INV, F.INV, and GAMMA.INV for other quantile functions
By mastering BETA.INV, you can build powerful statistical, Bayesian, and probability‑driven models in LibreOffice Calc.