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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

The following example shows how to use the beta_inv() function to return the inverse of the beta cumulative probability density function.

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().