Risk Measures of the ERNB Distribution Generated by G-NB Family

Emel Kizilok Kara; Sibel Acik Kemaloglu

doi:10.36753/mathenot.421706

EN

Risk Measures of the ERNB Distribution Generated by G-NB Family

Abstract

This paper provides VaR and CVaR risk measures, calculated for the Erlang-Negative Binomial (ERNB) distribution. The Erlang and negative binomial distributions are given and then ERNB distribution is obtained using a family of univariate distributions which is called G-Negative Binomial (G-NB). It is defined as compounding the negative binomial distribution (NB) with any continuous distribution (G). Here, we use the ERNB distribution obtained as taking Erlang distribution instead of G. In this paper, we focus on the estimation of VaR and CVaR risk measures for this distribution in closed form and the explicit expressions are also presented for some parameter values. The results are portrayed in the figures. In additionally, numerical examples are given to illustrate changing of the risk measure according to some parameters on a real data set of automobile insurance policies.

Keywords

Erlang distiribution,the Erlang-Negative Binomial distribution,Value at Risk,Conditional Value at Risk,G-NB family

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Emel Kizilok Kara

Sibel Acik Kemaloglu This is me

Publication Date

April 30, 2017

Submission Date

October 20, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 5 Number: 1

DOI

https://doi.org/10.36753/mathenot.421706

IZ

https://izlik.org/JA52NJ29TD

APA

Kara, E. K., & Kemaloglu, S. A. (2017). Risk Measures of the ERNB Distribution Generated by G-NB Family. Mathematical Sciences and Applications E-Notes, 5(1), 77-84. https://doi.org/10.36753/mathenot.421706

AMA

1.Kara EK, Kemaloglu SA. Risk Measures of the ERNB Distribution Generated by G-NB Family. Math. Sci. Appl. E-Notes. 2017;5(1):77-84. doi:10.36753/mathenot.421706

Chicago

Kara, Emel Kizilok, and Sibel Acik Kemaloglu. 2017. “Risk Measures of the ERNB Distribution Generated by G-NB Family”. Mathematical Sciences and Applications E-Notes 5 (1): 77-84. https://doi.org/10.36753/mathenot.421706.

EndNote

Kara EK, Kemaloglu SA (April 1, 2017) Risk Measures of the ERNB Distribution Generated by G-NB Family. Mathematical Sciences and Applications E-Notes 5 1 77–84.

IEEE

[1]E. K. Kara and S. A. Kemaloglu, “Risk Measures of the ERNB Distribution Generated by G-NB Family”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 77–84, Apr. 2017, doi: 10.36753/mathenot.421706.

ISNAD

Kara, Emel Kizilok - Kemaloglu, Sibel Acik. “Risk Measures of the ERNB Distribution Generated by G-NB Family”. Mathematical Sciences and Applications E-Notes 5/1 (April 1, 2017): 77-84. https://doi.org/10.36753/mathenot.421706.

JAMA

1.Kara EK, Kemaloglu SA. Risk Measures of the ERNB Distribution Generated by G-NB Family. Math. Sci. Appl. E-Notes. 2017;5:77–84.

MLA

Kara, Emel Kizilok, and Sibel Acik Kemaloglu. “Risk Measures of the ERNB Distribution Generated by G-NB Family”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, Apr. 2017, pp. 77-84, doi:10.36753/mathenot.421706.

Vancouver

1.Emel Kizilok Kara, Sibel Acik Kemaloglu. Risk Measures of the ERNB Distribution Generated by G-NB Family. Math. Sci. Appl. E-Notes. 2017 Apr. 1;5(1):77-84. doi:10.36753/mathenot.421706