The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models

doi:10.1007/s40305-021-00349-6

Journal of the Operations Research Society of China ›› 2022, Vol. 10 ›› Issue (1): 133-158.doi: 10.1007/s40305-021-00349-6

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The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models

Mahdi Rasekhi¹, Emrah Altun², Morad Alizadeh³, Haitham M. Yousof⁴

1 Department of Statistics, Malayer University, Malayer, Iran;
2 Department of Mathematics, Bartin University, Bartin, Turkey;
3 Department of Statistics, Persian Gulf University, Bushehr, Iran;
4 Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt

Received:2018-12-06 Revised:2021-04-04 Online:2022-03-30 Published:2022-03-23
Contact: Mahdi Rasekhi, Emrah Altun, Morad Alizadeh, Haitham M. Yousof E-mail:rasekhimahdi@gmail.com;emrahaltun@bartin.edu.tr;m.alizadeh@pgu.ac.ir;haitham.yousof@fcom.bu.edu.eg

Abstract

Abstract: A new generalization of the Weibull-G family is proposed with two extra shape parameters. The mathematical properties are derived in great detail. Using the Weibull and normal distributions as baseline distributions, two models are introduced. The first model is a location-scale regression model based on a new extension of the Weibull distribution. The second model is a new two-step financial risk model to forecast the daily value at risk. The flexibility and applicability of the proposed models are investigated by means of five real data sets on the lifetime and financial returns. Empirical findings of the study show that proposed models work well and produce better results than other well-known models for financial risk modeling and censored lifetime data analysis.

Key words: Odd log-logistic-G family, Weibull-G family, Regression model, Value at risk, Simulation, Maximum likelihood, Financial risk modeling

CLC Number:

62E15
62J05

Mahdi Rasekhi, Emrah Altun, Morad Alizadeh, Haitham M. Yousof. The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models[J]. Journal of the Operations Research Society of China, 2022, 10(1): 133-158.

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References

[1] Marshall, A.W., Olkin, I.:A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84(3), 641-652(1997)
[2] Gupta, R.C., Gupta, P.L., Gupta, R.D.:Modeling failure time data by Lehmann alternatives. Commun. Stat. Theory Methods 27, 887-904(1998)
[3] Cordeiro, G.M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E.M.M., Altun, E.:The generalized odd log-logistic family of distributions:properties, regression models and applications. J. Stat. Comput. Simul. 87(5), 908-932(2017)
[4] Haghbin, H., Ozel, G., Alizadeh, M., Hamedani, G.G.:A new generalized odd log-logistic family of distributions. Communication in Statistics-Theory and Methods. https://doi.org/10.1080/03610926. 2016.1222428(2016)
[5] Brito, E., Cordeiro, G.M., Yousof, H.M., Alizadeh, M., Silva, G.O.:The Topp-Leone odd log-logistic family of distributions. J. Stat. Comput. Simul. 87(15), 3040-3058(2017)
[6] Korkmaz, M.C., Yousof, H.M., Hamedani, G.G.:The exponential Lindley odd log-logistic-G family:properties, characterizations and applications. J. Stat. Theory Appl. 17(3), 554-571(2018)
[7] Alizadeh, M., Lak, F., Rasekhi, M., Ramires, T.G., Yousof, H.M., Altun, E.:The odd log-logistic Topp-Leone G family of distributions:heteroscedastic regression models and applications. Comput. Stat. 33(3), 1217-1244(2018a)
[8] Alizadeh, M., Yousof, H.M., Rasekhi, M., Altun, E.:The odd log-logistic Poisson-G Family of distributions. J. Math. Ext. 12(1), 81-104(2018b)
[9] Korkmaz, M.C., Yousof, H.M., Alizadeh, M., Hamedani, G.G.:The Topp-Leone generalized odd log-logistic family of distributions:properties, characterizations and applications. Commun Faculty Sci Univ Ankara Ser A1 Math Stat 68(2):1506-1527(2019)
[10] Alizadeh, M., Yousof, H.M., Jahanshahi, S.M.A., Najibi, S.M., Hamedani, G.G.:The transmuted odd log-logistic-G family of distributions. J. Stat. Manag. Syst. 23(4), 1-27(2020)
[11] Gleaton, J.U., Lynch, J.D.:On the distribution of the breaking strain of a bundle of brittle elastic fibers. Adv. Appl. Probab. 36, 98-115(2004)
[12] Gleaton, J.U., Lynch, J.D.:Properties of generalized log-logistic families of lifetime distributions. J. Probab. Stat. Sci. 4(1), 51-64(2006)
[13] Bourguignon, M., Silva, R.B., Cordeiro, G.M.:The Weibull-G family of probability distributions. J. Data Sci. 12, 53-68(2014)
[14] Arellano-Valle, R.B., Cortes, M.A., Gomez, H.W.:An extension of the epsilon-skew-normal distribution. Commun. Stat. Theory Methods 39(5), 912-922(2010)
[15] Rasekhi, M., Chinipardaz, R., Alavi, S.M.R.:A flexible generalization of the skew normal distribution based on a weighted normal distribution. Stat. Methods Appl. 25(3), 375-394(2016)
[16] Cont, R.:Empirical properties of asset returns:stylized facts and statistical issues. Quant. Finance 1, 223-236(2001)
[17] Bollerslev, T.:Generalized autoregressive conditional heteroskedasticity. J. Econom. 31(3), 307-327(1986)
[18] Bollerslev, T.:A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev. Econ. Stat. 69, 542-547(1987)
[19] Kupiec, P.H.:Techniques for verifying the accuracy of risk measurement models. J. Deriv. 3(2) (1995)
[20] Christoffersen, P.F.:Evaluating interval forecasts. Int. Econ. Rev. 39, 841-862(1998)
[21] Birnbaum, Z.W., Saunders, S.C.:Estimation for a family of life distributions with applications to fatigue. J. Appl. Probab. 6, 328-347(1969)
[22] Lee, C., Famoye, F., Olumolade, O.:Beta-Weibull distribution:some properties and applications to censored data. J. Mod. Appl. Stat. Methods 6, 173-186(2007)
[23] Sylwia,K.B.:Makehamsgeneraliseddistribution.Comput.MethodsSci.Technol. 13,113-120(2007)
[24] Cordeiro, G.M., de Castro, M.:A new family of generalized distributions. J. Stat. Comput. Simul. 81(7), 883-898(2011)
[25] Eugene, N., Lee, C., Famoye, F.:Beta-normal distribution and its applications. Commun. Stat. Theory Methods 31(4), 497-512(2002)
[26] Tahir, M.H., Cordeiro, G.M., Mansoor, M., Zubair, M.:The Weibull-Lomax distribution:properties and applications. Hacettepe J. Math. Stat. 44(2), 461-480(2015)
[27] Hosmer, D.W., Lemeshow, S.:Applied Survival Analysis:Regression Modeling of Time to Event Data. Wiley, New York (1998)

The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models

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