statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.pdf¶

KDEMultivariateConditional.pdf(endog_predict=None, exog_predict=None)[source]¶

Evaluate the probability density function.

Parameters:¶

endog_predict : array_like, optional¶

Evaluation data for the dependent variables. If unspecified, the training data is used.

exog_predict : array_like, optional¶

Evaluation data for the independent variables.

Returns:¶

pdf – The value of the probability density at endog_predict and exog_predict.

Return type:¶

array_like

Notes

The formula for the conditional probability density is:

\[f(y|x)=\frac{f(x,y)}{f(x)}\]

with

\[f(x)=\prod_{s=1}^{q}h_{s}^{-1}k \left(\frac{x_{is}-x_{js}}{h_{s}}\right)\]

where \(k\) is the appropriate kernel for each variable.