Estimation of the parameters of the kappa-Weibull distribution

The package of Matlab functions for estimating the parameters of the Kappa-Weibull distribution can be found here.

The function MAIN_KAPPA_WEIBULL calculates the fit of the data set DATA to the WEIBULL and the KAPPA Weibull distributions.  The empirical CDF of the data is first constructed.

The kappa-Weibull CDF fit is performed using the MLE method by minimization of the Negative Log-Likelihood (NLL) of the KAPPA Weibull distribution.

The optimization uses a two-step approach: First, it employs the function FMINCON using the ACTIVE-SET method and is then followed by FMINSEARCH (Simplex search method), which uses the output of FMINCON as initial condition.  Gradient information is supplied to FMINCON via the objective function lnL_wbk

Plots of the CDF for the empirical distribution as well as the best-fit Weibull and kappa-Weibull distributions are generated. The  functions  Phi(tau) (Weibull plots) for the three CDFs are also plotted. Finally, the quantile-quantile plot (empirical to kappa-Weibull) is generated.

The code has been tested with Matlab R2015b.

Copyright (C) 2022  Dionisis Hristopulos
 email: dchristopoulos@tuc.gr

 This bundle is free software; you can redistribute it and/or modify it
 under the terms of the GNU General Public License as published by the
 Free Software Foundation (version 2 of the License or  later version).

 This program is distributed WITHOUT ANY WARRANTY.
 See the GNU General Public License for more details.
 

If you use this software, please cite the publications:

[1] D.T. Hristopulos and A. Baxevani, “Kaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distribution,” Entropy, 24(10), 1362, 2022. https://doi.org/10.3390/e241013622022. https://doi.org/10.3390/e24101362

[2] D. T. Hristopulos, M. P. Petrakis, and G. Kaniadakis, “Finite-size effects on return interval distributions for weakest-link-scaling Systems,” Physical Review E 89, 052142, 28 May 2014. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.052142

[3] D. T. Hristopulos, M. P. Petrakis, and G. Kaniadakis, “Weakest-link scaling and extreme events in finite-sized systems,” Entropy, 17(3):1103-1122, 2015. https://doi.org/10.3390/e17031103

[4] Dionissios Hristopulos. (2022). Matlab code for estimating the parameters of the kappa-Weibull distribution (v1.0). Zenodo. doi.org/10.5281/zenodo.6942812