A New Generated Lifetime Model: Theory, Simulation and Application to Stress-Strength datasets
DOI:
https://doi.org/10.62933/w45q1k77Keywords:
Breaking Stress, Entropy , Skew-t Model , Simulation Study , Lifetime modelAbstract
In this article, a new continuous model called the exponentiated Gompertz generated skew- t (EGGST) distribution based on the exponentiated Gompertz generalized distribution is introduced. The new model is capable of fitting skewed, long and heavy tailed dataset and is more flexible than the skew-t distribution which is considered a special case. Related theoretical properties of the new model such as the quantile function, ordinary moment, probability weighted moment, order statistics, Rényi and Shannon entropies were investigated. The model parameters were estimated using the maximum likelihood estimation and simulation study carried out to examine the finite sample performance of these estimates. The applicability of the new model was illustrated by means of well-known breaking stress and strength datasets.
References
[1] Jones, M. C. (2001). A skew t distribution. In Probability and Statistical Models with Applications (eds C. A. Charalambides, M. V. Koutras and N. Balakrishnan), pp. 269–277. London: Chapman and Hall.
[2] Jones, M. C. & Faddy, M. J. (2003). A skew extension of the t distribution, with applications. J. Roy. Statist. Soc., Ser. B 65(2), 159–174.
[3] Jones, M. C. (2002). Student’s simplest distribution. The Statistician, 51(1), 41-49.
[4] Jones, M. C. (2004). Families of distributions of order statistics. Statistical Methodology, 6, 70-91.
[5] Gupta, A. K., Chang, F. C. & Huang, W. J. (2002). Some skew symmetric models. Random Oper. and Stoch. Eqn., 10, 133-140.
[6] Johnson, N. L., Kotz, S. & Balakrishnan, N. (1995). Continuous Univariate Distributions, vol. 2, 2nd edn. New York: Wiley.
[7] Arellano-Valle, R. B. & Genton, M. G. (2005). On the fundamental skew distributions. J. of Multiv. Anal., 96, 93-116.
[8] Sahu, S. K., Dey, D. K. & Branco, M. D. (2003). A new class of multivariate skew distributions with applications to Bayesian regression models. The Canadian Journal of Statistics, 31, 129–150.
[9] Azzalini, A. & Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J. Roy. Statist. Soc., B, 65, 367-389.
[10] Hasan, A. (2013). A Study of non-central skew-t Distributions and their Applications in Data Analysis and Change Point Detection, Ph.D. dissertation, Bowling Green State University, USA.
[11] Huang, W. J. & Chen, Y. H. (2006). Quadratic forms of multivariate skew normal-symmetric distributions. Statist. and Prob. Lett., 76, 871-879.
[12] Aas, K. & Haff, I. H. (2006). The Generalised Hyperbolic Skew Student’s t-distribution. Journal of Financial Econometric, 4(2), 275-309.
[13] Shafiei, S. & Doostparast, M. (2014). Balakrishnan skew-t distribution and associated statistical characteristics. Comm. Statist. Theory Methods, 43, 4109-4122.
[14] Shittu, O. I., Adepoju, K. A. & Adeniji, O. E. (2014). On the Beta Skew-t distribution in modelling stock return in Nigeria. International Journal of Modern Mathematical Sciences. 11(2), 94-102.
[15] Dikko, H. G & Agboola, S. (2017). Exponentiated generalized Skew-t distribution. Journal of the Nigerian Association of Mathematical Physics, 42, 219-228.
[16] Khamis, K. S., Basalamah, D., Ning, W., & Gupta, A. (2017). The Kumaraswamy Skew-t Distribution and Its Related Properties. Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2017.1346801
[17] Basalamah, D., Ning W. & Gupta A. (2018). The beta skew-t distribution and its properties. Journal of Statistical theory and practice, 12, 837-860.
[18] Adubisi, O. D., Abdulkadir, A. & Adubisi, C. E. (2022). A new hybrid form of the skew-t distribution: estimation methods comparison via Monte Carlo simulation and GARCH model application. Data Science in Finance and Economics, 2, 54-79.
[19] Adubisi, O. D., Abdulkadir, A. & Adashu, D. J. (2023). Improved parameter estimators for the flexible extended skew-t model with extensive simulations, applications and volatility modeling. Scientific African, 19, e01443.
[20] Adubisi, O. D., Abdulkadir, A, & Adubisi, C. E. (2025). The superiority of the EGARCH-odd exponentiated skew-t model in predicting financial returns volatility. Iranian Economic Review, 28(4), 1176-1202.
[21] Cordeiro, G. M., Alizadeh, M., Abraao, D. C., Nascimento O. & Rasekhi, M. (2016). The exponentiated Gompertz generated family of distributions: Properties and Applications, Chilean Journal of Statistics, 7(2), 29-50.
[22] Kenney, J. F. and Keeping, E. (1962). Mathematics of Statistics. D. Van Nostr and Company.
[23] Moor, J. J. (1988). A quantile alternative for Kurtosis. The Statistician, 37, 25-32.
[24] Greenwood, J. A., Landwehr, J. M., & Matalas, N. C. (1979). Probability weighted moments: Definitions and relations of parameters of several distributions expressible in inverse form. Water Resources Research, 15, 1049-1054.
[25] David, H. A. (1981). Order statistics, John Wiley & Sons, New York.
[26] Rényi, A. (1961). Proceeding of the fourth Berkeley symposium on mathematical statistics and probabilities. First Edition, University of California Press Berkeley.
[27] Nichols, M. D. & Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality Reliabil. Eng. Int., 22, 141-151.
[28] Reyad, H., Jamal, F., Othman, S. & Hamedani, G. G. (2018). The transmuted Gompertz-G family of distributions: properties and applications. Tbilisi Mathematical Journal, 11(3), 47-67.
[29] Yousof, H. M., Alizadeh, M., Jahanshahic, S. M., Ramires, T. G., Ghosh, I. & Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications. Journal of Data Science, 15, 723-740.
[30] Al-Aqtash, R., Lee, C. & Famoye, F. (2014). Gumbel-Weibull distribution: Properties and applications. J. Mod. Applied Stat. Methods, 13, 201-225.
[31] Cordeiro, G. M. & Lamonte, A. J. (2011). The Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Comput. Stat. Data Anal., 55, 1445-1461.
[32] Eghwerido, J. T., Nzei, L. C., David, I. J. & Adubisi, O. D. (2020). The Gompertz extended generalized exponential distribution: properties and applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1), 739-753.
[33] Reyad, H. M. & Othman, S. A. (2017). The Topp-Leone Burr-XII Distribution: Properties and Applications. British Journal of Mathematics & Computer Science, 21(5), 1-15.
[34] Merovci, F., Khaleel, M. A., Ibrahim, N. A. & Shitan, M. (2016). The beta type X distribution: properties with application, SpringerPlus, 5:697.
[35] Bourguignon, M., Silva, R. B. & Cordeiro, G. M. (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12: 53-68.
[36] Smith, R. L. & Naylor, J. C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36, 258-369.
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