Risk Analysis and Estimation of a Bimodal Heavy-Tailed Burr XII Model in Insurance Data: Exploring Multiple Methods and Applications

被引:17
作者
Yousof, Haitham M. [1 ]
Ansari, S. I. [2 ]
Tashkandy, Yusra [3 ]
Emam, Walid [3 ]
Ali, M. Masoom [4 ]
Ibrahim, Mohamed [5 ]
Alkhayyat, Salwa L. [6 ]
机构
[1] Benha Univ, Dept Stat Math & Insurance, Banha 13511, Egypt
[2] Azad Inst Engn & Technol, Dept Business Adm, Lucknow 226002, India
[3] King Saud Univ, Fac Sci, Dept Stat & Operat Res, POB 2455, Riyadh 11451, Saudi Arabia
[4] Ball State Univ, Dept Math Sci, Muncie, IN 47306 USA
[5] Damietta Univ, Fac Commerce, Dept Appl Math & Actuarial Stat, Dumyat 34517, Egypt
[6] Kafr El Sheikh Univ, Fac Commerce, Dept Stat Math & Insurance, Kafr Al Sheikh 33511, Egypt
关键词
Burr XII distribution; Cramer-Von-Mises; Kaplan-Meier; insurance claims; maximum likelihood; ordinary least square; risk exposure; risk analysis; weighted least square; simulation; REGRESSION-MODELS; GENERAL SYSTEM; DISTRIBUTIONS; FAMILY;
D O I
10.3390/math11092179
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Actuarial risks can be analyzed using heavy-tailed distributions, which provide adequate risk assessment. Key risk indicators, such as value-at-risk, tailed-value-at-risk (conditional tail expectation), tailed-variance, tailed-mean-variance, and mean excess loss function, are commonly used to evaluate risk exposure levels. In this study, we analyze actuarial risks using these five indicators, calculated using four different estimation methods: maximum likelihood, ordinary least square, weighted least square, and Cramer-Von-Mises. To achieve our main goal, we introduce and study a new distribution. Monte Carlo simulations are used to assess the performance of all estimation methods. We provide two real-life datasets with two applications to compare the classical methods and demonstrate the importance of the proposed model, evaluated via the maximum likelihood method. Finally, we evaluate and analyze actuarial risks using the abovementioned methods and five actuarial indicators based on bimodal insurance claim payments data.
引用
收藏
页数:26
相关论文
共 34 条
[1]   On the coherence of expected shortfall [J].
Acerbi, C ;
Tasche, D .
JOURNAL OF BANKING & FINANCE, 2002, 26 (07) :1487-1503
[2]  
Artzner P., 1999, N. Am. Actuar. J., V3, P11, DOI [DOI 10.1080/10920277.1999.10595795, 10.1080/10920277.1999.10595795]
[3]  
Beirlant J., 2004, N. Am. Actuar. J, V8, P108, DOI [DOI 10.1080/10920277.2004.10596140, 10.1080/10920277.2004.10596140]
[4]   ACQUISITION OF RESISTANCE IN GUINEA PIGS INFECTED WITH DIFFERENT DOSES OF VIRULENT TUBERCLE BACILLI [J].
BJERKEDAL, T .
AMERICAN JOURNAL OF HYGIENE, 1960, 72 (01) :130-148
[5]  
Burr I.W., 1973, COMMU STAT, P1, DOI [DOI 10.1080/03610927308827052, 10.1080/03610927308827052]
[6]   ON A GENERAL SYSTEM OF DISTRIBUTIONS .I. ITS CURVE-SHAPE CHARACTERISTICS .2. SAMPLE MEDIAN [J].
BURR, IW ;
CISLAK, PJ .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1968, 63 (322) :627-635
[8]   Cumulative frequency functions [J].
Burr, IW .
ANNALS OF MATHEMATICAL STATISTICS, 1942, 13 :215-232
[9]  
Charpentier A., 2014, Computational actuarial science with R
[10]  
Cooray K., 2005, SCAND ACTUAR J, DOI [10.1080/03461230510009763, DOI 10.1080/03461230510009763]