Modeling Censored Losses Using Splicing: A Global Fit Strategy with Mixed Erlang and Extreme Value Distributions

29 Pages Posted: 18 Nov 2016 Last revised: 17 May 2017

See all articles by Tom Reynkens

Tom Reynkens

KU Leuven - Department of Mathematics

Verbelen Roel

KU Leuven

Jan Beirlant

Catholic University of Leuven (KUL)

Katrien Antonio

KU Leuven; University of Amsterdam

Date Written: April 27, 2017

Abstract

In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modeling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data.

Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement.

Keywords: censoring, composite model, expectation-maximization algorithm, risk measurement, tail modeling

Suggested Citation

Reynkens, Tom and Roel, Verbelen and Beirlant, Jan and Antonio, Katrien, Modeling Censored Losses Using Splicing: A Global Fit Strategy with Mixed Erlang and Extreme Value Distributions (April 27, 2017). Available at SSRN: https://ssrn.com/abstract=2872107 or http://dx.doi.org/10.2139/ssrn.2872107

Tom Reynkens (Contact Author)

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Verbelen Roel

KU Leuven ( email )

Naamsestraat 69
B-3000 Leuven, Vlaams-Brabant 3000
Belgium

Jan Beirlant

Catholic University of Leuven (KUL) ( email )

W. de Croylaan 54
Leuven, B-3001
Belgium

Katrien Antonio

KU Leuven ( email )

Leuven, Vlaams-Brabant

HOME PAGE: http://www.econ.kuleuven.be/katrien.antonio

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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