Statistical analysis of the Lognormal-Pareto distribution using Probability Weighted Moments and Maximum Likelihood
AbstractThis paper deals with the estimation of the lognormal-Pareto and the lognormal-Generalized Pareto mixture distributions. The log-likelihood function is discontinuous, so that Maximum Likelihood Estimation is not asymptotically optimal. For this reason, we develop an alternative method based on Probability Weighted Moments. We show that the standard version of the method can be applied to the first distribution, but not to the latter. Thus, in the lognormal- Generalized Pareto case, we work out the details of a mixed approach combining Maximum Likelihood Estimation and Probability Weighted Moments. Extensive simulations give precise indications about the relative efficiencies of the methods in various setups. Finally, we apply the techniques to two real datasets in the actuarial and operational risk management fields.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Economics, University of Trento, Italia in its series Department of Economics Working Papers with number 1208.
Date of creation: 2012
Date of revision:
Probability Weighted Moments; Mixed Estimation Method; Lognormal-Pareto Distri- bution; Loss Models;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
- NEP-ECM-2012-09-09 (Econometrics)
- NEP-RMG-2012-09-09 (Risk Management)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Luciano Andreozzi).
If references are entirely missing, you can add them using this form.