The Exponentiated Rayleigh-Rayleigh Model on Peak over Threshold Method and Application to Danish Fire Claims
Keywords:
Exponentiated distribution, extreme value theorem, infinite mixture distribution, Rayleigh distribution, tailed distributionAbstract
This work introduces a new proposed model, the exponentiated Rayleigh-Rayleigh distribution
created by Rayleigh-Rayleigh and exponentiated distributions. It better fits the data sets, whereas
other distributions could not be implemented. The peak over threshold method is considered for model fitting in the tailed distribution. The parameters estimation is the maximum likelihood estimate and measurements of model fitting are the Kolmogorov-Smirnov test, Anderson-Darling test, Akaike Information Criterion and Bayesian information criterion. The exponentiated Rayleigh-Rayleigh distribution is compared to the current distributions, which are lognormal, gamma, Weibull and generalized Pareto, exponential, exponential-exponential, gamma-exponential and Rayleigh-Rayleigh. The data are considered based on simulation and Danish Fire data. We have found that the Exponentiated Rayleigh-Rayleigh distribution is the better fit for the small size of the data.
References
Abbas S, Mohsin M, Shahbaz SH, Shahbas MQ. Exponentiated Exponential - Exponentiated Weibull
Linear Mixed Distribution. Pak J Stat Oper Res. 2020; 16(3): 517- 527.
AL-Jammal ZY. Exponentiated exponential distribution as a failure time distribution. Iraqi J Stat Sci.
; (14): 63-75.
Al-Sulami D. Exponentiated exponential Weibull distribution, mathematical properties and application. Am J Appl Sci. 2020; 17: 188-195.
Al-Omari AI, Al-khazaleh AMH, Al-khazaleh M. Exponentiated new Weibull-Pareto distribution.
Revista Investigacion Operacional. 2019; 40(2): 165-175.
Boonradsamee J, Jaroengeratikun U, Bodhisuwan W. An optimal threshod selection approach for the
value at risk of the extreme events. Lobachevskii J Math. 2022; 43:23972410.
Coles S. An introduction to statistical modeling of extreme values. London: Springer-Verlag; 2001.
Cordeiro GM, Alizadeh M, Ortega EMM. The exponentiated half-logistic family of distributions:
properties and applications. J Probab Stat. 2014; 864396: 1-21.
Dankunprasert S. The modeling of claim severity with infinite mixture models for individual data of
motor insurance. MSc[Thesis]. Graduate School: Khon Kaen University; 2017.
Dankunprasert S, Jaroengeratikun U, Talangtam T. The properties of inverse Pareto distribution and
its application to extreme events. Thail Stat. 2021; 19(1): 1-12.
Elbatal GA, Raja AV. Transmuted exponentiated Frechet distribution: properties and applications. J
Stat Appl Probab. 2014; 3(3):379-394.
Embrechts P, Klppelberg C, Mikosch T. Modelling extremal events for insurance and finance. Budapest: Springer-Verlag; 1997.
Fatima K, Jan U, Ahmad SP. Statistical properties and applications of the exponentiated inverse Kumaraswamy distribution. J Reliab Stat Stud. 2018; 11(1):93-102.
Gupta R.D, Kundu D. Theory & methods: generalized exponential distributions. Aust NZ J Stat.
; 41: 173-188.
Gupta RD, Kundu D. Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical J. 2001; 43(1): 117130.
Hamedani GH. Characterizations of exponentiated distributions. Pak J Stat Oper Res. 2013; 9(1):
-24.
Handique L, Chakraborty S, Andrade TAN. The exponentiated generalized Marshall-Olkin family of
distribution: its properties and applications. Ann Data Sci. Springer. 2018; 6(3): 391-411.
Iqbal Z, Wasim M, Riaz N. Exponentiated moment exponential distribution and power series distribution with applications: a new compound family. Int J Adv Res. 2017; 5(7): 1335-1355.
Jaroengeratikun U, Dankunprasert S, Talangtam T. Infinite mixture of Rayleigh-Rayleigh distribution
and its application to motor insurance claims. Pak J Stat Oper Res. 2022; 16: 517-527.
Klugman SA, Panjer HH, Willmot GE. Loss models from data to decisions, third edition.
Canada:John Wiley Sons, Inc; 2008.
Masoom M, Pal M, and Woo J. Some exponentiated distributions. Commun Stat Appl Methods. 2007;
(1): 93-109.
Mohammed AS, Ugwuowo FI. The transmuted exponential-exponential distribution with application
to breast cancer data. Pak J Stat. 2021; 37(1): 1-18.
Okorie IE, Akpanta AC, and Ohakwe J. The exponentiated Gumbel Type-2 distribution: properties
and application. Int J Math Math Sci. 2016; 1-10.
Poga’ny TK, Saboor A. The Gamma exponentiated exponentialWeibull distribution. Faculty of Sciences and Mathematics: Serbia University of Nis, Serbia; 2016.
Shaymal CH. Comparing different estimation methods of generalized Pareto distribution (GPD) and
their limitations. MSc[Thesis]. Lamar University; 2014.
Wasinrat S, Choopradit B. The Poisson inverse Pareto distribution and its application. Thail Stat.
; 21(1):110124.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
