Loss Data Analysis with Maximum Entropy

  • Erika Gomes-Gonçalves
  • Henryk Gzyl
  • Silvia Mayoral


We present some results of the application of maximum entropy methods to determine the probability density of compound random variables. This problem is very important in the banking and insurance business, but also appears in system reliability and in operations research.

The mathematical tool consists of inverting Laplace transforms of positive compound random variables using the maximum entropy method. This method needs a very small number of (real) values of the Laplace transform, is robust, works with small data sets, and it can be extended to include errors in the data as well as data specified up to intervals.

In symbols, the basic typical problem consist in determining the density fS of a compound random variable like \(S = \sum _{n=1}^N X_n\), or that of a sum of such random variables. There, N is an integer random variable and Xn is a sequence of positive, continuous random variables, independent among themselves and of N. Our methodology can be applied to determine the probability density of the total loss S and that of the individual losses.


Loss distributions Sample dependence Maximum entropy 


  1. 1.
    Gomes-Gonçalves, E., Gzyl, H., Mayoral, S.: Loss Data Analysis: The Maximum Entropy Approach. De Gruyter, Berlin (2018)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Erika Gomes-Gonçalves
    • 1
  • Henryk Gzyl
    • 2
  • Silvia Mayoral
    • 3
  1. 1.Independent ConsultantMadridSpain
  2. 2.Instituto de Estudios Superiores de Administración - IESACaracasVenezuela
  3. 3.Univ. Carlos III, MadridDepartment of Business AdministrationMadridSpain

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