lpdf

Beta.lpdf(X)

Log of the Probability Density Function (LPDF).

The log-PDF for the four-parameter beta distribution is:

\[\ln f(x | \alpha, \beta, a, b) &= (\alpha - 1) \cdot \ln(x - a) + (\beta - 1) \cdot \ln(b - x) \ &\quad - (\alpha + \beta - 1) \cdot \ln(b - a) - \ln B(\alpha, \beta)\]

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)}`

XArrayLike

The input data points at which to evaluate the LPDF.

NDArray[np.float64]

The log-PDF values corresponding to each point in X.