pdf

Beta.pdf(X)

Probability density function (PDF).

The PDF for the four-parameter beta distribution is:

\[f(x | \alpha, \beta, a, b) = \frac{(x - a)^(\alpha - 1) \cdot (b - x)^(\beta - 1)} { (b - a)^(\alpha + \beta - 1) \cdot B(\alpha, \beta)}\]

where \(a\) is the lower_bound parameter, \(b\) is the upper_bound parameter, \(\alpha\) is the first shape parameter and \(\beta\) is the second shape parameter,:math:`B(alpha, beta) =

rac{Gamma(alpha)Gamma(beta)}{Gamma(alpha + beta)}`

is the Beta function.

XArrayLike

The input data points at which to evaluate the PDF.

NDArray[np.float64]

The PDF values corresponding to each point in X.