An Extended Kumaraswamy-Gull Alpha Power Exponential Distribution: Properties and Application to Real Data

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-8
Year of Publication : 2022
Authors : Mohamed Kpangay, Leo O. Odongo, George O. Orwa
 10.14445/22315373/IJMTT-V68I8P508

How to Cite?

Mohamed Kpangay, Leo O. Odongo, George O. Orwa, "An Extended Kumaraswamy-Gull Alpha Power Exponential Distribution: Properties and Application to Real Data," International Journal of Mathematics Trends and Technology, vol. 68, no. 8, pp. 72-104, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I8P508

Abstract
This paper proposes a four-parameterized distribution, namely an extended Kumaraswamy-Gull Alpha Power Exponential distribution. The proposed distribution gives rise to some well-known sub-models. Some basic properties of the distribution are derived. The method of maximum likelihood estimation was employed to estimate the parameters of the distribution. A Monte Carlo simulation study was conducted to evaluate the performance of the MLE estimates. From the simulation results, it is observed that with an increase in sample size the average estimates approach the true value of the parameters, and the average bias, MSE, and RMSE decrease, in general. The proposed K-GAPE distribution is fitted to two real data sets and compared to its sub-models. A conclusion can be made that the purposed distribution performs better than its underlying sub-models.

Keywords : Exponential distribution, Gull Alpha Power Family, Kumaraswamy distribution, Maximum likelihood estimation.

Reference

[1] R. D. Gupta, D. Kundu, Exponentiated exponential family: an alternative to gamma and weibull distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences 43 (1) (2001) 117–130.
[2] R. D. Gupta, D. Kundu, Generalized exponential distribution: Existing results and some recent developments, Journal of Statistical planning and inference 137 (11) (2007) 3537–3547.
[3] M. Ijaz, S. M. Asim, Lomax exponential distribution with an application to real-life data, PloS one 14 (12) (2019) e0225827.
[4] K. Modi, D. Kumar, Y. Singh, A new family of distribution with application on two real datasets on survival problem, Science & Technology Asia 25 (1) (2020) 1–10.
[5] G. M. Cordeiro, E. M. Ortega, D. C. da Cunha, The exponentiated generalized class of distributions, Journal of data science 11 (1) (2013) 1–27.
[6] G. M. Cordeiro, M. Alizadeh, T. G. Ramires, E. M. Ortega, The generalized odd half-cauchy family of distributions: properties and applications, Communications in Statistics-Theory and Methods 46 (11) (2017) 5685–5705.
[7] I. Ghosh, S. Nadarajah, On some further properties and application of weibull-r family of distributions, Annals of Data Science 5 (3) (2018) 387–399.
[8] M. H. Tahir, G. M. Cordeiro, M. Alizadeh, M. Mansoor, M. Zubair, G. G. Hamedani, The odd generalized exponential family of distributions with applications, Journal of Statistical Distributions and Applications 2 (1) (2015) 1–28.
[9] M. Alizadeh, M. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, G. Hamedani, The kumaraswamy marshal-olkin family of distributions, Journal of the Egyptian Mathematical Society 23 (3) (2015) 546–557.
[10] A. Z. Afifya, G. M. Cordeiro, H. M. Yousof, Z. M. Nofal, A. Alzaatreh, The kumaraswamy transmuted-g family of distributions: properties and applications, Journal of Data Science 14 (2) (2016) 245–270.
[11] S. Chakraborty, L. Handique, The generalized marshall-olkinkumaraswamy-g family of distributions, Journal of data Science 15 (3) (2017) 391–422.
[12] M. E. Mead, A. Afify, N. S. Butt, The modified kumaraswamy weibull distribution: Properties and applications in reliability and engineering sciences, Pakistan Journal of Statistics and Operation Research 16 (3) (2020) 433–446.
[13] M. Ijaz, S. M. Asim, M. Farooq, S. A. Khan, S. Manzoor, A gull alpha power weibull distribution with applications to real and simulated data, Plos one 15 (6) (2020) e0233080.
[14] C. B. Ampadu, Gull alpha power of the chen type, Pharmacovigil and Pharmacoepi 3 (2) (2020) 16–17.
[15] C. B. Ampadu, Gull alpha power of the ampadu-type: Properties and applications, Earthline Journal of Mathematical Sciences 6 (1) (2021) 187–207.
[16] M. Kilai, G. A. Waititu, W. A. Kibira, M. Abd El-Raouf, T. A. Abushal, A new versatile modification of the rayleigh distribution for modeling covid-19 mortality rates, Results in Physics 35 (2022) 105260.
[17] M. Kilai, G. A. Waititu, W. A. Kibira, H. M. Alshanbari, M. ElMorshedy, A new generalization of gull alpha power family of distributions with application to modeling covid-19 mortality rates, Results in Physics 36 (2022) 105339.
[18] H. A. Khogeer, A. Alrumayh, M. Abd El-Raouf, M. Kilai, R. Aldallal, Exponentiated gull alpha exponential distribution with application to covid-19 data, Journal of Mathematics 2022 (2022).
[19] G. M. Cordeiro, M. de Castro, A new family of generalized distributions, Journal of statistical computation and simulation 81 (7) (2011) 883–898.
[20] J. F. Kenney, E. Keeping, Linear regression and correlation, Mathematics of statistics 1 (1962) 252–285.
[21] J. Moors, A quantile alternative for kurtosis, Journal of the Royal Statistical Society: Series D (The Statistician) 37 (1) (1988) 25–32.
[22] A. Renyi, On measures of entropy and information, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, Vol. 4, University of California Press, 1961, pp. 547–562. 
[23] R. D. Gupta, D. Kundu, Theory & methods: Generalized exponential distributions, Australian & New Zealand Journal of Statistics 41 (2) (1999) 173–188.
[24] K. Adepoju, O. Chukwu, Maximum likelihood estimation of the kumaraswamy exponential distribution with applications, Journal of Modern Applied Statistical Methods 14 (1) (2015) 18.
[25] M. V. Aarset, How to identify a bathtub hazard rate, IEEE transactions on reliability 36 (1) (1987) 106–108.