chaospy.approximate_density

chaospy.approximate_density(distribution, idx, xloc, cache=None, step_size=1e-07)

Approximate the probability density function.

Args:

distribution (Distribution):

Distribution in question. May not be an advanced variable.

idx (int):

The dimension to take approximation along.

xloc (numpy.ndarray):

Location coordinates. Requires that xloc.shape=(len(distribution), K).

cache (Optional[Dict[Distribution, Tuple[numpy.ndarray, numpy.ndarray]]]):

Current state in the evaluation graph. If omitted, assume that evaluations should be done from scratch.

step_size (float):

The relative step size between two points used to calculate the derivative.

Returns:

numpy.ndarray: Local probability density function with

out.shape == xloc.shape. To calculate actual density function, evaluate numpy.prod(out, 0).

Example:

>>> distribution = chaospy.Normal(1000, 10)
>>> xloc = numpy.array([990, 1000, 1010])
>>> approximate_density(distribution, 0, xloc).round(4)
array([0.0242, 0.0399, 0.0242])
>>> distribution.pdf(xloc).round(4)
array([0.0242, 0.0399, 0.0242])