Dönüştürülmüş Weibull Dağılımı için Risk Ölçülerinin Tahmini

Abstract

Bu çalışmada dönüştürülmüş Weibull dağılımı için bazı risk ölçülerinin tahmini problemini ele aldık. Bu bağlamda risk ölçülerini tahmin edebilmek için en çok olabilirlik yöntemi kullanıldı. Ayrıca risk ölçülerinin en çok olabilirlik tahmin edicilerinin asimptotik dağılımlarına dayalı yaklaşık güven aralıkları elde ettik. Sonrasında, bu tahmin edicilerin farklı örnek hacimleri ve parametre değerlerinde performanslarını değerlendirmek için geniş bir Monte Carlo benzetim çalışması tasarladık.

Keywords

• Risk ölçüleri; Dönüştürülmüş Weibull dağılımı; Nokta tahmini; Aralık tahmini.

Estimation of Risk Measures for Transmuted Weibull Distribution

Abstract

In this paper, we tackle a problem of the estimation of some risk measures for transmuted Weibull distribution. In this regard, the maximum likelihood method is used to estimate the risk measures. We also obtain asymptotic confidence intervals based on the asymptotic distributions of maximum likelihood estimators of risk measures. Then, we consider a comprehensive Monte Carlo simulation study to assess the performances of these estimators at different sample sizes and parameter settings.

Keywords

• Risk Measures
• Transmuted Weibull Distribution
• Point Estimation
• Interval Estimation

References

1. [1] Aryal, G.R., Tsokos, C.P., Transmuted Weibull distribution: a generalization of theWeibull probability distribution, European Journal of Pure and Applied Mathematics, 4(2), 89-102, 2011.
2. [2] Shaw, W.T., Buckley, I.R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv:0901.0434, 2009.
3. [3] Khan, M.S., King, R., Hudson, I.L., Transmuted Weibull distribution: properties and estimation, Communications in Statistics-Theory and Methods, 46(11), 5394-5418, 2017.
4. [4] Dowd, K., Blake, D., After VaR: the theory, estimation, and insurance applications of quantile‐based risk measures. Journal of Risk and Insurance, 73(2), 193-229, 2006.
5. [5] Artzner, P., Application of coherent risk measures to capital requirements in insurance, North American Actuarial Journal 2(2), 11–25, 1999.
6. [6] Afify, A.Z., Gemeay, A.M., Ibrahim, N.A. The heavy-tailed exponential distribution: Risk measures, estimation, and application to actuarial data, Mathematics, 8(8) 1276, doi:10.3390/math8081276, 2020.
7. [7] Tanış, C., On transmuted power function distribution: characterization, risk measures, and estimation, Journal of New Theory, (34), 72-81, 2021.
8. [8] Klugman, S.A., Panjer, H.H., Willmot, G.E., Loss models: from data to decisions, vol. 715, John Wiley & Sons, 2012.

9. [9] Al-Babtain, A.A., Gemeay, A.M., Afify, A.Z., Estimation methods for the discrete poisson-lindley and discrete lindley distributions with actuarial measures and applications in medicine,, Journal of King Saud University, 33(2), 1-11, 2020. https://doi.org/10.1016/j.jksus.2020.10.021.
10. [10] Landsman, Z., On the tail mean–variance optimal portfolio selection, Insurance: Mathematics and Economics, 46, 547–553, 2010.