Araştırma Makalesi
BibTex RIS Kaynak Göster

Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application

Yıl 2023, Cilt: 52 Sayı: 4, 1082 - 1095, 15.08.2023

Rahele Mollaie Mehdi Jabbari Nooghabi

Öz

In this paper, a Pareto distribution in the presence of outliers is proposed as a claim size distribution. The shrinkage estimators of the shape parameter $\alpha$ are derived. Also, estimators of Premium are considered and compared by using simulation study. Finally, an actual example is proposed for obtaining different estimators of the Premium.

Anahtar Kelimeler

Pareto distribution maximum likelihood moment method Shrinkage estimator uniformly minimum variance unbiased outliers premium insurance

Kaynakça

  • [1] V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd ed., Wiley, New York, 1994.
  • [2] G. Benktander, A note on the most “dangerous” and skewest class of distribution, Astin Bull. 2, 87–390, 1963.
  • [3] S.K. Bhattacharya and V.K. Srivastava, A preliminary test procedure in life testing, J. Amer. Statist. Assoc. 69 (347), 726-729, 1974.
  • [4] U.J. Dixit, Characterization of the gamma distribution in the presence of k outliers, Bull. Bombay Mathematical Colloquium 4, 54–59, 1987.
  • [5] U.J. Dixit, Estimation of parameters of the gamma distribution in the presence of outliers, Comm. Statist. Theory Methods 18 (8), 3071–3085, 1989.
  • [6] U.J. Dixit and M. Jabbari Nooghabi, Efficient estimation in the Pareto distribution, Stat. Methodol. 7 (6), 687–691, 2010.
  • [7] U.J. Dixit and M. Jabbari Nooghabi, Efficient estimation in the Pareto distribution with the presence of outliers, Stat. Methodol. 8 (4), 340–355, 2011.
  • [8] U.J. Dixit and F.P. Nasiri, Estimation of parameters of the exponential distribution in the presence of outliers generated from uniform distribution, Metron 49 (3-4), 187–198, 2001.
  • [9] M. Ebegil and S. Ozdemir, Two different shrinkage estimator classes for the shape parameter of classical Pareto distribution, Hacet. J. Math. Stat. 45 (4), 1231–1244, 2016.
  • [10] F.E. Grubbs, Procedures for detecting outlying observations in samples, Technometrics 11 (1), 1–21, 1969.
  • [11] D.M. Hawkins, Identification of Outliers, Chapman and Hall, London, 1980.
  • [12] S. Heilpern, A rank-dependent generalization of zero utility principle, Insur.: Math. Econ. 33 (1), 67–73, 2003.
  • [13] M. Jabbari Nooghabi, On detecting outliers in the Pareto distribution, J. Stat. Comput. Simul. 89 (8), 1466–1481, 2019.
  • [14] M. Jabbari Nooghabi, Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers, Environmetrics 32 (5), e2676, 1-12, 2021.
  • [15] M. Jabbari Nooghabi and E. Khaleghpanah Nooghabi, On entropy of a Pareto distribution in the presence of outliers, Comm. Statist. Theory Methods 45 (17), 5234– 5250, 2016.
  • [16] M. Jabbari Nooghabi and M. Naderi, Stressstrength reliability inference for the Pareto distribution with outliers, J. Comput. Appl. Math. 404, 113911, 1-17, 2022.
  • [17] R.G. Miller, Simultaneous Statistical Inference, 2nd ed., Springer Verlag, New York, 1981.
  • [18] K. Okhli and M. Jabbari Nooghabi, On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers, Appl. Math. Comput. 392, 125712, 1-11, 2021.
  • [19] V. Pareto, Cours DEconomie Politique, Vol. 2, Book 3, Lausanne, 1897.
  • [20] R.E. Quandt, Old and new methods of estimation and the Pareto distribution, Metrika 10, 55–82, 1966.
  • [21] M. Rytgaard, Estimation in Pareto distribution, Nordisk Reinsurance company, Gronniugen 25, Dk-1270 Compenhagen. K, Denmark, 1990.
  • [22] A. Tsanakas and E. Desli, Risk measures and theories of choice, Br. Actuar. J. 9 (4), 959–991, 2003.
  • [23] V. Young, Premium Principles In Encyclopedia of Actuarial Science, Wiley, New York, 2004.

Yıl 2023, Cilt: 52 Sayı: 4, 1082 - 1095, 15.08.2023

Rahele Mollaie Mehdi Jabbari Nooghabi

Öz

Kaynakça

  • [1] V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd ed., Wiley, New York, 1994.
  • [2] G. Benktander, A note on the most “dangerous” and skewest class of distribution, Astin Bull. 2, 87–390, 1963.
  • [3] S.K. Bhattacharya and V.K. Srivastava, A preliminary test procedure in life testing, J. Amer. Statist. Assoc. 69 (347), 726-729, 1974.
  • [4] U.J. Dixit, Characterization of the gamma distribution in the presence of k outliers, Bull. Bombay Mathematical Colloquium 4, 54–59, 1987.
  • [5] U.J. Dixit, Estimation of parameters of the gamma distribution in the presence of outliers, Comm. Statist. Theory Methods 18 (8), 3071–3085, 1989.
  • [6] U.J. Dixit and M. Jabbari Nooghabi, Efficient estimation in the Pareto distribution, Stat. Methodol. 7 (6), 687–691, 2010.
  • [7] U.J. Dixit and M. Jabbari Nooghabi, Efficient estimation in the Pareto distribution with the presence of outliers, Stat. Methodol. 8 (4), 340–355, 2011.
  • [8] U.J. Dixit and F.P. Nasiri, Estimation of parameters of the exponential distribution in the presence of outliers generated from uniform distribution, Metron 49 (3-4), 187–198, 2001.
  • [9] M. Ebegil and S. Ozdemir, Two different shrinkage estimator classes for the shape parameter of classical Pareto distribution, Hacet. J. Math. Stat. 45 (4), 1231–1244, 2016.
  • [10] F.E. Grubbs, Procedures for detecting outlying observations in samples, Technometrics 11 (1), 1–21, 1969.
  • [11] D.M. Hawkins, Identification of Outliers, Chapman and Hall, London, 1980.
  • [12] S. Heilpern, A rank-dependent generalization of zero utility principle, Insur.: Math. Econ. 33 (1), 67–73, 2003.
  • [13] M. Jabbari Nooghabi, On detecting outliers in the Pareto distribution, J. Stat. Comput. Simul. 89 (8), 1466–1481, 2019.
  • [14] M. Jabbari Nooghabi, Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers, Environmetrics 32 (5), e2676, 1-12, 2021.
  • [15] M. Jabbari Nooghabi and E. Khaleghpanah Nooghabi, On entropy of a Pareto distribution in the presence of outliers, Comm. Statist. Theory Methods 45 (17), 5234– 5250, 2016.
  • [16] M. Jabbari Nooghabi and M. Naderi, Stressstrength reliability inference for the Pareto distribution with outliers, J. Comput. Appl. Math. 404, 113911, 1-17, 2022.
  • [17] R.G. Miller, Simultaneous Statistical Inference, 2nd ed., Springer Verlag, New York, 1981.
  • [18] K. Okhli and M. Jabbari Nooghabi, On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers, Appl. Math. Comput. 392, 125712, 1-11, 2021.
  • [19] V. Pareto, Cours DEconomie Politique, Vol. 2, Book 3, Lausanne, 1897.
  • [20] R.E. Quandt, Old and new methods of estimation and the Pareto distribution, Metrika 10, 55–82, 1966.
  • [21] M. Rytgaard, Estimation in Pareto distribution, Nordisk Reinsurance company, Gronniugen 25, Dk-1270 Compenhagen. K, Denmark, 1990.
  • [22] A. Tsanakas and E. Desli, Risk measures and theories of choice, Br. Actuar. J. 9 (4), 959–991, 2003.
  • [23] V. Young, Premium Principles In Encyclopedia of Actuarial Science, Wiley, New York, 2004.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Rahele Mollaie 0000-0003-1334-3662

Mehdi Jabbari Nooghabi 0000-0002-5636-2209

Yayımlanma Tarihi 15 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 4

Kaynak Göster

APA Mollaie, R., & Jabbari Nooghabi, M. (2023). Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application. Hacettepe Journal of Mathematics and Statistics, 52(4), 1082-1095.
AMA Mollaie R, Jabbari Nooghabi M. Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application. Hacettepe Journal of Mathematics and Statistics. Ağustos 2023;52(4):1082-1095.
Chicago Mollaie, Rahele, ve Mehdi Jabbari Nooghabi. “Shrinkage Estimators of Shape Parameter of Contaminated Pareto Model With Insurance Application”. Hacettepe Journal of Mathematics and Statistics 52, sy. 4 (Ağustos 2023): 1082-95.
EndNote Mollaie R, Jabbari Nooghabi M (01 Ağustos 2023) Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application. Hacettepe Journal of Mathematics and Statistics 52 4 1082–1095.
IEEE R. Mollaie ve M. Jabbari Nooghabi, “Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 4, ss. 1082–1095, 2023.
ISNAD Mollaie, Rahele - Jabbari Nooghabi, Mehdi. “Shrinkage Estimators of Shape Parameter of Contaminated Pareto Model With Insurance Application”. Hacettepe Journal of Mathematics and Statistics 52/4 (Ağustos 2023), 1082-1095.
JAMA Mollaie R, Jabbari Nooghabi M. Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application. Hacettepe Journal of Mathematics and Statistics. 2023;52:1082–1095.
MLA Mollaie, Rahele ve Mehdi Jabbari Nooghabi. “Shrinkage Estimators of Shape Parameter of Contaminated Pareto Model With Insurance Application”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 4, 2023, ss. 1082-95.
Vancouver Mollaie R, Jabbari Nooghabi M. Shrinkage estimators of shape parameter of contaminated Pareto model with insurance application. Hacettepe Journal of Mathematics and Statistics. 2023;52(4):1082-95.

For more information about the journal, please visit: https://dergipark.org.tr/en/pub/hujms