lpdf

Pareto.lpdf(X)

Log of the Probability Density Function (LPDF).

The log-PDF for the two-parameter Pareto distribution is:

\[\ln f(x | \alpha, \beta) = \alpha \ln \beta + \ln \alpha - (\alpha + 1) \ln x\]

where \(\alpha\) is the shape parameter and \(\beta\) is the scale parameter. The log-density is \(-\infty\) for \(x < \beta\).

Parameters:

X (ArrayLike) – The input data points at which to evaluate the LPDF.

Returns:

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

Return type:

NDArray[np.float64]