Cumulants¶
This module provides functions to compute cumulants of discrete functions. Additionally functions are provided to compute cumulants from moments and vice versa
- discrete_cumulant(func, cumulant, stencil)¶
Computes cumulant of discrete function.
- Parameters:
func – sequence of function components, has to have the same length as stencil
cumulant – definition of cumulant, either as an index tuple, or as a polynomial (similar to moment description)
stencil – sequence of directions
- cumulants_from_pdfs(stencil, cumulant_indices=None, pdf_symbols=None)¶
Transformation of pdfs (or other discrete function on a stencil) to cumulant space.
- Parameters:
stencil – stencil object
cumulant_indices – sequence of cumulant indices, could be tuples or polynomial representation if left to default and a full stencil was passed, the full set i.e.
moments_up_to_component_order
with ‘order=2’ is usedpdf_symbols – symbolic values for pdf values, if not passed they default to \(f_0, f_1, ...\)
- Returns:
dict mapping cumulant index to expression
- cumulant_as_function_of_raw_moments(index, moments_dict=None)¶
Returns an expression for the cumulant of given index as a function of raw moments.
- Parameters:
index – a tuple of same length as spatial dimensions, specifying the cumulant
moments_dict – a dictionary that maps moment indices to symbols/values. These values are used for the moments in the returned expression. If this parameter is None, default symbols are used.
- raw_moment_as_function_of_cumulants(index, cumulants_dict=None)¶
Inverse transformation of
cumulant_as_function_of_raw_moments()
.
- cumulant_as_function_of_central_moments(index, moments_dict=None)¶
Same as
cumulant_as_function_of_raw_moments()
but with central instead of raw moments.
- central_moment_as_function_of_cumulants(index, cumulants_dict=None)¶
Same as
raw_moment_as_function_of_cumulants()
but with central instead of raw moments.