beta_inv()

Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Returns the inverse of the beta cumulative probability density function.

If probability = beta_cdf(x,...), then beta_inv(probability,...) = x.

The beta distribution can be used in project planning to model probable completion times given an expected completion time and variability.

Syntax

beta_inv(probability,alpha,beta)

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
probability	int, long, or real	✔️	A probability associated with the beta distribution.
alpha	int, long, or real	✔️	A parameter of the distribution.
beta	int, long, or real	✔️	A parameter of the distribution.

Returns

The inverse of the beta cumulative probability density function beta_cdf()

Note

• If any argument is nonnumeric, the function returns null.
• If alpha ≤ 0 or beta ≤ 0, the function returns null.
• If probability ≤ 0 or probability > 1, the function returns NaN.
• Given a value for probability, beta_inv() seeks that value x such that beta_cdf(x, alpha, beta) = probability.

Examples

Run the query

datatable(p:double, alpha:double, beta:double, comment:string)
[
    0.1, 10.0, 20.0, "Valid input",
    1.5, 10.0, 20.0, "p > 1, yields null",
    0.1, double(-1.0), 20.0, "alpha is < 0, yields NaN"
]
| extend b = beta_inv(p, alpha, beta)

Output

p	alpha	beta	comment	b
0.1	10	20	Valid input	0.226415022388749
1.5	10	20	p > 1, yields null
0.1	-1	20	alpha is < 0, yields NaN	NaN

Related content

• For computing cumulative beta distribution function, see beta-cdf().
• For computing probability beta density function, see beta-pdf().