beta_pdf()

Returns the probability density beta function.

beta_pdf(0.2, 10.0, 50.0)

The beta distribution is commonly used to study variation in the percentage of something across samples, such as the fraction of the day people spend watching television.

Syntax

beta_pdf(x, alpha, beta)

Arguments

  • x: A value at which to evaluate the function.
  • alpha: A parameter of the distribution.
  • beta: A parameter of the distribution.

Returns

Notes

If any argument is nonnumeric, beta_pdf() returns null value.

If x ≤ 0 or 1 ≤ x, beta_pdf() returns NaN value.

If alpha ≤ 0 or beta ≤ 0, beta_pdf() returns the NaN value.

Examples

datatable(x:double, alpha:double, beta:double, comment:string)
[
    0.5, 10.0, 20.0, "Valid input",
    1.5, 10.0, 20.0, "x > 1, yields NaN",
    double(-10), 10.0, 20.0, "x < 0, yields NaN",
    0.1, double(-1.0), 20.0, "alpha is < 0, yields NaN"
]
| extend r = beta_pdf(x, alpha, beta)
x alpha beta comment r
0.5 10 20 Valid input 0.746176019310951
1.5 10 20 x > 1, yields NaN NaN
-10 10 20 x < 0, yields NaN NaN
0.1 -1 20 alpha is < 0, yields NaN NaN

References

  • For computing the inverse of the beta cumulative probability density function, see beta-inv().
  • For the standard cumulative beta distribution function, see beta-cdf().