Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics

Nikolay Kyurkchiev

doi:doi:10.11648/j.ijtam.20160202.13

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Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics

Nikolay Kyurkchiev

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 13 September 2016 Accepted: 22 October 2016 Published: 25 November 2016

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Abstract

In this paper we study the uniform approximation of the generalized cut function by sigmoidal Erlang cumulative distribution function (Ecdf). The results are relevant for applied insurance mathematics and are intended for the actuary when preparing the strategy “Insurance responsibility”. Numerical examples are presented using CAS MATHEMATICA.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.13
Page(s)	40-44
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Erlang Cumulative Distribution Function (Ecdf), Generalized Cut Function Associated to the (Ecdf), Uniform Approximation

References

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[5]	Behncke H., Insurance Mathematics, Univ. Press, 2000, Osnabruck.
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[9]	Kyurkchiev, N., S. Markov, On the Hausdorff distance between the Heaviside step function and Verhulst logistic function, J. Math. Chem., vol. 54 (1), 2016, pp. 109–119, doi:10.1007/S10910-015-0552-0.
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[11]	Iliev, A., N. Kyurkchiev, S. Markov, On the approximation of the cut and step functions by logistic and Gompertz functions, Biomath, vol. 4 (2), 2015, pp. 2–13.
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Nikolay Kyurkchiev. (2016). Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. International Journal of Theoretical and Applied Mathematics, 2(2), 40-44. https://doi.org/10.11648/j.ijtam.20160202.13

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ACS Style

Nikolay Kyurkchiev. Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. Int. J. Theor. Appl. Math. 2016, 2(2), 40-44. doi: 10.11648/j.ijtam.20160202.13

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AMA Style

Nikolay Kyurkchiev. Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. Int J Theor Appl Math. 2016;2(2):40-44. doi: 10.11648/j.ijtam.20160202.13

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@article{10.11648/j.ijtam.20160202.13,
  author = {Nikolay Kyurkchiev},
  title = {Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {40-44},
  doi = {10.11648/j.ijtam.20160202.13},
  url = {https://doi.org/10.11648/j.ijtam.20160202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.13},
  abstract = {In this paper we study the uniform approximation of the generalized cut function by sigmoidal Erlang cumulative distribution function (Ecdf). The results are relevant for applied insurance mathematics and are intended for the actuary when preparing the strategy “Insurance responsibility”. Numerical examples are presented using CAS MATHEMATICA.},
 year = {2016}
}

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TY  - JOUR
T1  - Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics
AU  - Nikolay Kyurkchiev
Y1  - 2016/11/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.13
DO  - 10.11648/j.ijtam.20160202.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 40
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.13
AB  - In this paper we study the uniform approximation of the generalized cut function by sigmoidal Erlang cumulative distribution function (Ecdf). The results are relevant for applied insurance mathematics and are intended for the actuary when preparing the strategy “Insurance responsibility”. Numerical examples are presented using CAS MATHEMATICA.
VL  - 2
IS  - 2
ER  -

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Author Information

Nikolay Kyurkchiev

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

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APA Style

Nikolay Kyurkchiev. (2016). Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. International Journal of Theoretical and Applied Mathematics, 2(2), 40-44. https://doi.org/10.11648/j.ijtam.20160202.13

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ACS Style

Nikolay Kyurkchiev. Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. Int. J. Theor. Appl. Math. 2016, 2(2), 40-44. doi: 10.11648/j.ijtam.20160202.13

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AMA Style

Nikolay Kyurkchiev. Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics. Int J Theor Appl Math. 2016;2(2):40-44. doi: 10.11648/j.ijtam.20160202.13

Copy | Download

@article{10.11648/j.ijtam.20160202.13,
  author = {Nikolay Kyurkchiev},
  title = {Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {40-44},
  doi = {10.11648/j.ijtam.20160202.13},
  url = {https://doi.org/10.11648/j.ijtam.20160202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.13},
  abstract = {In this paper we study the uniform approximation of the generalized cut function by sigmoidal Erlang cumulative distribution function (Ecdf). The results are relevant for applied insurance mathematics and are intended for the actuary when preparing the strategy “Insurance responsibility”. Numerical examples are presented using CAS MATHEMATICA.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Uniform Approximation of the Generalized Cut Function by Erlang Cumulative Distribution Function and Application in Applied Insurance Mathematics
AU  - Nikolay Kyurkchiev
Y1  - 2016/11/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.13
DO  - 10.11648/j.ijtam.20160202.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 40
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.13
AB  - In this paper we study the uniform approximation of the generalized cut function by sigmoidal Erlang cumulative distribution function (Ecdf). The results are relevant for applied insurance mathematics and are intended for the actuary when preparing the strategy “Insurance responsibility”. Numerical examples are presented using CAS MATHEMATICA.
VL  - 2
IS  - 2
ER  -

Copy | Download