A Study on Inverted Exponentiated Generalized Skew Student T Distribution: Definition, Properties and Estimation with Application to Financial Data

Danjuma Idi, Danjuma Jibasen, Okolo Abraham, Emmanuel Torsen

Abstract


This article aims to derive a new generalization of the exponentiated generalized family of distribution and with it a sub model called the Inverted Exponentiated Generalized Skew Student t distribution (IEGSStD) for modeling financial data. Some statistical properties of the IEGSStD are derived, such as quantile function, raw moments, entropy, reliability function, and hazard function. Parameter estimates using maximum likelihood estimation were consistent and the behavior of the estimates with increase in sample size was studied using Montecarlo simulation. In a practical application to the simple returns of two financial idiocies, the Guaranty Trust Holding Company PLC (GTCO) and Nigeria Breweries (NB). The flexibility of the Inverted Exponentiated Generalized Skew Student t distribution demonstrated by application to the simple returns revealed that the Inverted Exponentiated Generalized Skew Student t model yielded a better fit.


Full Text:

PDF

References


Al-Omari, A. I., Al-khazaleh, A. M., & Al-khazaleh, M. (2019). Exponentiated New Weibull-Pareto Distribution. Investigacion operacional, 40(2), 165-176.

Ashour, S. K., & Eltehiwy, M. A. (2015). Exponentiated power Lindley distribution. Journal of advanced research, 6(6), 895-905.

Cordeiro, G. M., Ortega, E. M., & da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.

David I. J., Mathew S. & Falgore J. Y., (2024). New Sine Inverted Exponential Distribution: properties, Simulation and Application. European Journal of Statistics. 4(5), 1-14.

Dikko, H. G., & Agboola, S. (2017a). Statistical Properties of Exponentiated Skewed Student-t Distributions. Journal of the Nigeria Association of Mathematical Physics, 4(7), 251-260.

Dikko, H.G and Agboola, S (2017b) “Statistical Properties of Exponentiated Generalized Skewed Student-t Distributions”. Nigeria Association of Mathematical Physics (NAMP) 42; 219-228.

Fatima, K., & Ahmad, S. P. (2017). The Exponentiated Inverted Exponential Distribution. Journal of Applied Information Science Volume, 5(01).

Fattah, A. A., Nadarajah, S., & Ahmed, A. H. N. (2017). The exponentiated transmuted Weibull geometric distribution with application in survival analysis. Communications in Statistics: Simulation and Computation, 46(6), 4244-4263.

Hassan, A. S., & Abd-Allah, M. (2018). Exponentiated Weibull-Lomax distribution: properties and estimation. Journal of Data Science, 16(2), 277-298.

Jones, M. C, & M. J. Faddy, (2003). A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65:159-174

Lemonte, J., Barreto-Souza, W. & Cordeiro G. M. (2013). The exponentiated Kumaraswamy distribution and its log-transform, Brazilian. Journal of Probability and Statistics 27(4): 31-53.

Mathew S., John, D. I., & Mutah, Y. (2024). A Study on One-Parameter Entropy-Transformed Exponential Distribution and Its Application. Journal of Reliability and Statistical Studies, Vol. 17(1), 17–44.

Mohammed, A. S., & Ugwuowo, F. I. (2020). A New Family of Distributions for Generating Skewed Models: Properties and Applications. Pakistan Journal of Statistics, 36(2).

Muhammad, M., & Liu, L. (2019). A new extension of the generalized half logistic distribution with applications to real data. Entropy, 21(4), 339.

Rather, A. A., & Subramanian, C. (2018). Exponentiated Mukherjee-Islam Distribution. Journal of Statistics Applications & Probability, 7(2), 357-361.

Rather, A. A., Subramanian, C., Al-Omari, A. I., & Alanzi, A. R. (2022). Exponentiated Ailamujia distribution with statistical inference and applications of medical data. Journal of Statistics and Management Systems, 25(4), 907-925.


Refbacks

  • There are currently no refbacks.