lpdf

Cauchy.lpdf(X)

Log of the Probability Density Function (LPDF).

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

\[\ln f(x | \alpha, \beta) = \ln(\gamma) - \ln(\pi \cdot ((x - \alpha)^2 + \beta^2))\]

where \(\alpha\) is the location parameter and \(\beta\) is the scale parameter.

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]