Unit Exponentiated Fréchet Distribution: Actuarial Measures, Quantile Regression and Applications

Abdul Ghaniyyu Abubakari1, Albert Luguterah2, Suleman Nasiru2
1C. K. Tedam University of Technology and Applied Sciences
2Department of Statistics, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aarset MV (1987) How to identify a bathtub hazard rate. IEEE Trans Reliab 36(1):106–108

Altun E, Cordeiro GM (2020) The unit-improved second-degree Lindley distribution: inference and regression modeling. Comput Stat 35(1):259–279

Altun E, Hamedani G (2018) The log-xgamma distribution with inference and application. Journal De La Societe Française De Statistique 159(3):40–55

Altun E, El-Morshedy M, Eliwa MS (2021) A new regression model for bounded response variable: an alternative to the b eta and unit-Lindley regression models. PLoS ONE 16(1):1–15

Artikis T, Voudouri A, Artikis P (2001) Properties and applications in risk frequency reduction operations of an integral part model. Comput Math Appl 42(1–2):211–218

Artzner P (1999) Application of coherent risk measures to capital requirements in insurance. North Am Actuar J 3(2):11–25

Bantan RAR, Jamal F, Chesneau C, Elgarhy M (2021) Theory and applications of the unit Gamma/Gompertz distribution. Mathematics 9(16):1850. https://doi.org/10.3390/math9161850

Barlow RE, Campo R (1975) Total time on test processes and applications to failure data analysis. In: Reliability and fault tree analysis. Society for Industrial and Applied Mathematics, pp 451–481

Bolker B (2014) Tools for general maximum likelihood estimation. R Development Core Team

Cheng R, Amin N (1979) Maximum product of spacings estimation with application to the lognormal distribution. Mathematical report 79-1. Cardiff University of Wales IST

Consul PC, Jain GC (1971) On the log-Gamma distribution and its properties. Statistische Hefte 12(2):100–106

Cox DR, Snell EJ (1968) A general defiition of residuals. J Roy Stat Soc Ser B (methodol) 30(2):248–265

Dunn PK, Smyth GK (1996) Randomized quantile residuals. J Comput Graph Stat 5(3):236–244

Embrechts P, Resnick SI, Samorodnitsky G (1999) Extreme value theory as a risk management tool. North Am Actuar J 3:30–41

Esscher F (1932) On the probability function in the collective theory of risk. Scand Actuar J 15:175–195

Ferrari S, Cribari-Neto F (2004) Beta regression for modelling rates and proportions. J Appl Stat 31(7):799–815

Furman E, Landsman Z (2006) Tail variance premium with applications for elliptical portfolio of risks. ASTIN Bull J IAA 36(2):433–462

Gómez-Déniz E, Sordo MA, Calderın-Ojeda E (2014) The log–Lindley distribution as an alternative to the beta regression model with applications in insurance. Insur Math Econ 54:49–57

Grassia A (1977) On a family of distributions with argument between 0 and 1 obtained by transformation of the Gamma and derived compound distributions. Aust J Stat 19(2):108–114

Gündüz S, Korkmaz MC (2020) A new unit distribution based on the unbounded Johnson distribution rule: the unit Johnson SU distribution. Pakistan J Stat Oper Res 471–490

Jodrá P (2020) A bounded distribution derived from the shifted Gompertz law. J King Saud Univ Sci 32(1):523–536

Johnson NL (1949) Systems of frequency curves generated by methods of translation. Biometrika 36(1/2):149–176

Klugman SA, Panjer HH, Willmot GE (2012) Loss models: from data to decisions, vol 715. Wiley

Korkmaz MC, Chesneau C (2021) On the unit Burr-XII distribution with the quantile regression modeling and applications. Comput Appl Math 40(1):1–26

Korkmaz MC, Chesneau C, Korkmaz ZS (2021) On the arcsecant hyperbolic normal distribution: properties, quantile regression, modeling and applications. Symmetry 13(1):117

Kumaraswamy P (1980) A generalized probability density function for double bounded random processes. J Hydrol 46(1–2):79–88

Lee ET, Wang J (2003) Statistical methods for survival data analysis, vol 476. Wiley

Lindsay BG, Li B (1997) On second-order optimality of the observed Fisher information. Ann Stat 25:2172–2199

Lukito C, Novita M, Sari SF (2019) Risk measurement for investment using tail variance premium and tail standard deviation premium. In: AIP conference proceedings, vol 2184. AIP Publishing LLC.

Mazucheli J, Menezes AFB, Chakraborty S (2019) On the one parameter unit-Lindley distribution and its associated regression model for proportion data. J Appl Stat 46(4):700–714

Mazucheli J, Menezes AFB, Fernandes LB, de Oliveira RP, Ghitany ME (2020) The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. J Appl Stat 47(6):954–974

Mitnik PA, Baek S (2013) The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation. Stat Pap 54:177–192

Nadarajah S, Kotz S (2003) The exponentiated fr´echet distribution. Interstat Electron J 14:01–07

Saito S (2014) Introduction to the premium principle based on the Wang transform. In: A mathematical approach to research problems of science and technology. Springer, pp 207–217

Schmit JT, Roth K (1990) Cost effectiveness of risk managements practice. J Risk Insur 57(3):455–470

Shaked M, Shanthikumar JG (2007) Stochastic orders. Wiley, New York

Topp CW, Leone FC (1955) A family of J-shaped frequency functions. J Am Stat Assoc 50(269):209–219

Xiang Y, Gubian S, Suomela B, Hoeng J (2013) Generalized simulated annealing: GenSA package. R J 5(1):13–29

Zubair A, Eisa M, Gholamhossein H (2019) A family of loss distributions with an application to the vehicle insurance loss data. Pakistan J Stat Oper Res. https://doi.org/10.18187/pjsor.v15i3.2995