Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data

Richard Onyino Simwa; Martin Mutwiri Kithinji; Joseph Anthony McOtteku Otieno

doi:doi:10.11648/j.ijsd.20160203.11

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Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data

Richard Onyino Simwa, Martin Mutwiri Kithinji, Joseph Anthony McOtteku Otieno

Published in International Journal of Statistical Distributions and Applications (Volume 2, Issue 3)

Received: 20 July 2016 Accepted: 24 September 2016 Published: 28 October 2016

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Abstract

The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.

Published in	International Journal of Statistical Distributions and Applications (Volume 2, Issue 3)
DOI	10.11648/j.ijsd.20160203.11
Page(s)	27-34
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), 2016. Published by Science Publishing Group

Keywords

Burr XII Mixture Distribution, Unemployment Insurace, Capital Asset Pricing Model, Taxable Wage Base, Discounted Cash Flow, Mean Present Value, Premium Rate

References

[1]	Actuarial Education Company (2013), ST4: “Pensions and other Benefits Specialist Technical”, The Institute and Faculty of Actuaries.
[2]	Beenstock, M. (1985). Competitive Unemployment Insurance Pricing. Geneva Papers on Risk and Insurance, 23-31.
[3]	Bowers, N. (1980). Probing the issues of unemployment duration. Monthly Labor Review, 103(7), 23-32.
[4]	Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1997). Actuarial Mathematics (Illinois: The Society of Actuaries).
[5]	Bronars, S. G. (1985). Fair Pricing of Unemployment Insurance Premiums. Journal of Business, 27-47.
[6]	Chuang, H. L., & Yu, M. T. (2010). Pricing Unemployment Insurance–An Unemployment-Duration-Adjusted Approach. Astin Bulletin, 40(02), 519-545.
[7]	Cummins, J. D. (1991). Statistical and financial models of insurance pricing and the insurance firm. The Journal of Risk and Insurance, 58(2), 261-302.
[8]	Feller, W. (1968). An introduction to probability theory and its applications: volume I (Vol. 3). London-New York-Sydney-Toronto: John Wiley & Sons.
[9]	Malinvaud, E. (1985). Unemployment insurance. Geneva Papers on Risk and Insurance, 6-22.
[10]	McDonald, J. B., & Butler, R. J. (1987). Some generalized mixture distributions with an application to unemployment duration. The Review of Economics and Statistics, 232-240.
[11]	Okasha, M. K., & Matter (2015), M. Y. ON THE THREE-PARAMETER BURR TYPE XII DISTRIBUTION AND ITS APPLICATION TO HEAVY TAILED LIFETIME DATA. Journal: JOURNAL OF ADVANCES IN MATHEMATICS, 10(4).
[12]	Salant, S. W. (1977). Search theory and duration data: a theory of sorts. The Quarterly Journal of Economics, 39-57.
[13]	Board of Governors of the Federal Reserve System (US), 3-Month Treasury Constant Maturity Rate [DGS3MO], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/seriesDGS3MO, June 16, 2016.
[14]	Standards and Poors data: www.econ.yale.edu/~shiller/data/ie_data.xl
[15]	US. Bureau of Labor Statistics, Average (Mean) Duration of Unemployment [UEMPMEAN], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/seriesUEMPMEAN, June 16, 2016.
[16]	US. Employment and Training Administration, Initial Claims [ICNSA], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/ICNSA, June 16, 2016.
[17]	US. Employment and Training Administration, Covered Employment [COVEMP], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/COVEMP, June 30, 2016.

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APA Style

Richard Onyino Simwa, Martin Mutwiri Kithinji, Joseph Anthony McOtteku Otieno. (2016). Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. International Journal of Statistical Distributions and Applications, 2(3), 27-34. https://doi.org/10.11648/j.ijsd.20160203.11

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ACS Style

Richard Onyino Simwa; Martin Mutwiri Kithinji; Joseph Anthony McOtteku Otieno. Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. Int. J. Stat. Distrib. Appl. 2016, 2(3), 27-34. doi: 10.11648/j.ijsd.20160203.11

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AMA Style

Richard Onyino Simwa, Martin Mutwiri Kithinji, Joseph Anthony McOtteku Otieno. Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. Int J Stat Distrib Appl. 2016;2(3):27-34. doi: 10.11648/j.ijsd.20160203.11

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@article{10.11648/j.ijsd.20160203.11,
  author = {Richard Onyino Simwa and Martin Mutwiri Kithinji and Joseph Anthony McOtteku Otieno},
  title = {Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {3},
  pages = {27-34},
  doi = {10.11648/j.ijsd.20160203.11},
  url = {https://doi.org/10.11648/j.ijsd.20160203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160203.11},
  abstract = {The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.},
 year = {2016}
}

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TY  - JOUR
T1  - Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data
AU  - Richard Onyino Simwa
AU  - Martin Mutwiri Kithinji
AU  - Joseph Anthony McOtteku Otieno
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160203.11
DO  - 10.11648/j.ijsd.20160203.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 27
EP  - 34
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160203.11
AB  - The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.
VL  - 2
IS  - 3
ER  -

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Author Information

Richard Onyino Simwa

School of Mathematics, University of Nairobi, Nairobi, Kenya
Martin Mutwiri Kithinji

School of Mathematics, University of Nairobi, Nairobi, Kenya
Joseph Anthony McOtteku Otieno

School of Mathematics, University of Nairobi, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Richard Onyino Simwa, Martin Mutwiri Kithinji, Joseph Anthony McOtteku Otieno. (2016). Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. International Journal of Statistical Distributions and Applications, 2(3), 27-34. https://doi.org/10.11648/j.ijsd.20160203.11

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ACS Style

Richard Onyino Simwa; Martin Mutwiri Kithinji; Joseph Anthony McOtteku Otieno. Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. Int. J. Stat. Distrib. Appl. 2016, 2(3), 27-34. doi: 10.11648/j.ijsd.20160203.11

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AMA Style

Richard Onyino Simwa, Martin Mutwiri Kithinji, Joseph Anthony McOtteku Otieno. Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data. Int J Stat Distrib Appl. 2016;2(3):27-34. doi: 10.11648/j.ijsd.20160203.11

Copy | Download

@article{10.11648/j.ijsd.20160203.11,
  author = {Richard Onyino Simwa and Martin Mutwiri Kithinji and Joseph Anthony McOtteku Otieno},
  title = {Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {3},
  pages = {27-34},
  doi = {10.11648/j.ijsd.20160203.11},
  url = {https://doi.org/10.11648/j.ijsd.20160203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160203.11},
  abstract = {The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Application of Burr XII Mixture Distributions to Model Unemployment Duration in Pricing Unemployment Insurance Assuming USA Data
AU  - Richard Onyino Simwa
AU  - Martin Mutwiri Kithinji
AU  - Joseph Anthony McOtteku Otieno
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160203.11
DO  - 10.11648/j.ijsd.20160203.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 27
EP  - 34
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160203.11
AB  - The objective of this research is to consider varying unemployment duration in the pricing of unemployment insurance with application to USA data. The study assumes that unemployment duration follows Burr XII mixture distribution while the discount rate to use in the pricing of the scheme will bedetermined by fitting market data into the capital asset pricing model. The Burr XII mixture distribution has been used to model unemployment duration in order to allow for heterogeniety in the unemployment duration of the insured employees. The results yield a mean unemployment duration of approximately 16 weeks and premium contribution rate of 5.10% of the taxable wage base per month for a benefit of 45% of the taxable wage base per month payable on weekly basis during spells of unemployment.
VL  - 2
IS  - 3
ER  -

Copy | Download