Parameters¶
-
jumpdiff.parameters.
jump_amplitude
(moments: numpy.ndarray, tol: float = 1e-10, full: bool = False, verbose: bool = False) → numpy.ndarray¶ Retrieves the jump amplitude xi (\(\xi\)) via
\[\lambda(x,t) = \frac{M_4(x,t)}{3\sigma_{\xi}^4}.\]Take notice that the different normalisation of the
moments
leads to a different results.Parameters: - moments (np.ndarray) – Moments extracted with the function
moments
. Needs moments up to order6
. - tol (float (defaul
1e-10
)) – Toleration for the division of the moments. - full (bool (defaul
False
)) – IfTrue
returns also the (biased) weighed standard deviation of the averaging process. - verbose (bool (defaul
True
)) – Prints the result.
Returns: xi_est – Estimator of the jump amplitude xi (\(\xi\)).
Return type: np.ndarray
References
Anvari, M., Tabar, M. R. R., Peinke, J., Lehnertz, K., ‘Disentangling the stochastic behavior of complex time series.’ Scientific Reports, 6, 35435, 2016. doi: 10.1038/srep35435.
Lehnertz, K., Zabawa, L., and Tabar, M. R. R., ‘Characterizing abrupt transitions in stochastic dynamics.’ New Journal of Physics, 20(11):113043, 2018. doi: 10.1088/1367-2630/aaf0d7.
- moments (np.ndarray) – Moments extracted with the function
-
jumpdiff.parameters.
jump_rate
(moments: numpy.ndarray, xi_est: numpy.ndarray = None, tol: float = 1e-10, full: bool = False, verbose: bool = False) → numpy.ndarray¶ Retrieves the jump rate lamb (\(\lambda\)) via
\[\sigma_{\xi}^2 = \frac{M_6(x,t)}{5M_4(x,t)}.\]Take notice that the different normalisation of the
moments
leads to a different results.Parameters: - moments (np.ndarray) – moments extracted with the function ‘moments’. Needs moments of order 6.
- tol (float (defaul
1e-10
)) – Toleration for the division of the moments. - full (bool (defaul
False
)) – IfTrue
returns also the (biased) weighed standard deviation of the averaging process. - verbose (bool (defaul
True
)) – Prints the result.
Returns: xi_est – Estimator on the jump rate lamb (\(\lambda\))
Return type: np.ndarray
References
Anvari, M., Tabar, M. R. R., Peinke, J., Lehnertz, K., ‘Disentangling the stochastic behavior of complex time series.’ Scientific Reports, 6, 35435, 2016. doi: 10.1038/srep35435.
Lehnertz, K., Zabawa, L., and Tabar, M. R. R., ‘Characterizing abrupt transitions in stochastic dynamics.’ New Journal of Physics, 20(11):113043, 2018. doi: 10.1088/1367-2630/aaf0d7.