Abstract
Purpose- The purpose
of this study is to focus on forecasting the total claim distribution of
fire-disaster and transportation insurances by combining probabilities of claim
distribution using the data for 2014 and 2015.
Methodology- In this
study, the combination of Weibull and Gamma distributions of fire-disaster and
transport policies are discussed. By combining two different probability
density function (PDF), a single PDF is derived and thus it is aimed to provide
convenience in calculations.
Findings- Two
probability distributions were combined with mathematical methods. As a result,
a single probability density function was obtained. This
probability density function can represent the total claim distribution.
Conclusion- In conclusion, we used the data regarding
fire-disaster and transportation insurances for 2014 and 2015. Insurance firms
that offer these two policies to their customers need to determine their risk
taking into consideration the total claim distribution from the policies. Since
Weibull and Gamma distributions have a PDF, it is necessary to integrate the
multiplication of the characteristic functions for combining these two
distributions. The PDF obtained as a result of mathematical operations is the
PDF of the total claim distribution.
Keywords
Claim distributions combining probability distributions insurance total claim distribution actuarial models.
References
- Armutlu, İ. H. (1999). İşletme istatistiğine giriş. Beta Basım Yayım Dağıtım.
- Benckert, L. G., Jung, J. (1974). Statistical models of claim distributions in fire insurance. ASTIN Bulletin: The Journal of the IAA, 8(1), 1-25.
- Clemen, R. T., Winkler, R. L. (1999). Combining probability distributions from experts in risk analysis. Risk analysis, 19(2), 187-203.
- Çekici, M. E., İnel, M. N. (2013). Türk sigorta sektörünün direkt prim üretimlerinin tahmin teknikleri ile incelenmesi. Marmara Üniversitesi İ.İ.B. Dergisi, 34(1), 135-152.
- Eısekberg, E., Gale, D. (1959). Consensus of subjective probabilities: the pari-mutuel method. Ann. Math. Statist. Vol. 30 (1959), pp. 165-168.
- Genest, C., Zidek, J. V. (1986). Combining probability distributions: a critique and an annotated bibliography. Statistical Science, 1(1), 114-135.
- Hill, T. P., Miller, J. (2011). How to combine independent data sets for the same quantity. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21.3 (2011): 033102-1.
- Hill, T. (2011). Conflations of probability distributions. Transactions of the American Mathematical Society 363.6 (2011): 3351-3372.
- Liu, X., Ghorpade, A., Tu, Y. L., Zhang, W. J. (2012). A novel approach to probability distribution aggregation. Information Sciences, 188 (2012), 269-275.
- McMillan, R. W., Barnes, N. P. (1976). Detection of optical pulses: the effect of atmospheric scintillation. Applied Optics, Vol. 15, No. 10, Ekim 1976.
- McMillan, R. W., Kohlberg, I. (2017). A simple method for combining probability distribution functions relevant to radar and communications systems. IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS), (2017).
- Morrıs, P. A. (1974). Decision analysis expert use. Management Sci., Vol. 20 (1974), pp. 1233-1241.
- Pırıldak, M., Esensoy, Ö. Bağımli riskler için toplam hasar miktarinin dağilimi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 1(1), 68-79.
- Roberts, H. V. (1965). Probabilistic prediction. J. Amer. Statist. Assoc., Vol. 60 (1965), pp. 50-62.
- Stone, M. (1961). The opinion pool. Ann. Math. Statist., Vol. 32 (1961), 1339-1342.
- Tse, Y. K. (2009). Nonlife actuarial models: theory, methods and evaluation. Cambridge University Press.
- Winkler, R. L. (1968). The consensus of subjective probability distributions. Management Sci., Vol. 15 (1968), pp. B61-B75. www.hazine.gov.tr
Abstract
References
- Armutlu, İ. H. (1999). İşletme istatistiğine giriş. Beta Basım Yayım Dağıtım.
- Benckert, L. G., Jung, J. (1974). Statistical models of claim distributions in fire insurance. ASTIN Bulletin: The Journal of the IAA, 8(1), 1-25.
- Clemen, R. T., Winkler, R. L. (1999). Combining probability distributions from experts in risk analysis. Risk analysis, 19(2), 187-203.
- Çekici, M. E., İnel, M. N. (2013). Türk sigorta sektörünün direkt prim üretimlerinin tahmin teknikleri ile incelenmesi. Marmara Üniversitesi İ.İ.B. Dergisi, 34(1), 135-152.
- Eısekberg, E., Gale, D. (1959). Consensus of subjective probabilities: the pari-mutuel method. Ann. Math. Statist. Vol. 30 (1959), pp. 165-168.
- Genest, C., Zidek, J. V. (1986). Combining probability distributions: a critique and an annotated bibliography. Statistical Science, 1(1), 114-135.
- Hill, T. P., Miller, J. (2011). How to combine independent data sets for the same quantity. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21.3 (2011): 033102-1.
- Hill, T. (2011). Conflations of probability distributions. Transactions of the American Mathematical Society 363.6 (2011): 3351-3372.
- Liu, X., Ghorpade, A., Tu, Y. L., Zhang, W. J. (2012). A novel approach to probability distribution aggregation. Information Sciences, 188 (2012), 269-275.
- McMillan, R. W., Barnes, N. P. (1976). Detection of optical pulses: the effect of atmospheric scintillation. Applied Optics, Vol. 15, No. 10, Ekim 1976.
- McMillan, R. W., Kohlberg, I. (2017). A simple method for combining probability distribution functions relevant to radar and communications systems. IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS), (2017).
- Morrıs, P. A. (1974). Decision analysis expert use. Management Sci., Vol. 20 (1974), pp. 1233-1241.
- Pırıldak, M., Esensoy, Ö. Bağımli riskler için toplam hasar miktarinin dağilimi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 1(1), 68-79.
- Roberts, H. V. (1965). Probabilistic prediction. J. Amer. Statist. Assoc., Vol. 60 (1965), pp. 50-62.
- Stone, M. (1961). The opinion pool. Ann. Math. Statist., Vol. 32 (1961), 1339-1342.
- Tse, Y. K. (2009). Nonlife actuarial models: theory, methods and evaluation. Cambridge University Press.
- Winkler, R. L. (1968). The consensus of subjective probability distributions. Management Sci., Vol. 15 (1968), pp. B61-B75. www.hazine.gov.tr
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | September 30, 2018 |
| Published in Issue | Year 2018 Volume: 7 Issue: 3 |
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