Estimation of Parameters of Topp-Leone Inverse Lomax Distribution in Presence of Right Censored Samples

Year 2021, Volume: 34 Issue: 4, 1193 - 1208, 01.12.2021

Amal Soliman Doaa Ismail

https://doi.org/10.35378/gujs.773645

Cited By: 7

Abstract

In this paper, we deal with a three-parameter inverse Lomax cited as the Topp-Leone inverse Lomax (TLIL) distribution depend on Topp-Leone-G family. Expressions of its density and distribution functions are explored. The structure properties of suggested model are provided like quantile function, moments, incomplete moments and Rényi entropy. Maximum likelihood estimators of the TLIL distribution parameters along with reliability estimator are worked out via complete and type II censored samples. To investigate the statistical properties of estimates we present numerical illustration along with two real data.

Keywords

Inverse lomax, Topp-Leone family, Maximum likelihood, Censored samples

Supporting Institution

Modern Academy for Engineering and technology Maadi

References

• [1] Kleiber, C., Kotz, S., “Statistical size distributions in economics and actuarial sciences”, Wiley, New York, (2003).
• [2] Kleiber, C., “Lorenz ordering of order statistics from log-logistic and related distributions”, Journal of Statistical Planning and Inference, 120: 13-19, (2004).
• [3] McKenzie, D., Miller, C., Falk, D. A.,“The Landscape ecology of fire”, Springer, New York, (2011).
• [4] Rahman, J. Aslam, M., Ali, S., “Estimation and prediction of inverse Lomax model via Bayesian approach”, Caspian Journal of Applied Science Research, 3: 43-56, (2013).
• [5] Rahman, J., Aslam, M., “Interval prediction of future order statistics in two component mixture inverse Lomax model: A Bayesian approach”, American Journal of Mathematical and Management Science, 33(3): 216-227, (2014).
• [6] Singh, S. K., Singh, U., Yadav, A. S., “Reliability estimation for inverse Lomax distribution under type Π censored data using Markov chain Monte Carlo method”, International Journal of Mathematics and Statistics, 17(1): 128-146, (2016).
• [7] Jan, U. Ahmad., “Bayesian analysis of inverse Lomax distribution using approximation techniques”, Mathematical Theory and Modeling, 7(7): 1-12, (2017).
• [8] Bantan, R. A. R., Elgarhy, M., Chesneau, C. and Jamal, F., “Estimation of entropy for inverse Lomax distribution under multiple censored data”, Entropy, 22(601): 1-15, (2020).
• [9] Hassan, A.S., Abd-Allah, M., On the inverse power Lomax distribution”, Annals of Data Science, 6: 259–278, (2018).
• [10] Hassan, A.S., Mohamed, R.E., “Weibull inverse Lomax distribution”, Pakistan Journal of Statistics and Operation Research”, 15: 587–603, (2019).
• [11] Hassan, A.S., Mohamed, R.E., “Parameter estimation for inverted exponentiated Lomax distribution with right censored data”, Gazi University Journal of Science, 32(4): 1370-1386, (2019).
• [12] ZeinEldin, R.A., Haq, M.A.U., Hashmi, S., Elsehety, M., “Alpha power transformed inverse Lomax distribution with different methods of estimation and applications”, Complexity, 1–15, (2020).
• [13] Maxwell, O., Chukwu, A.U., Oyamakin, O.S., Khaleel, M.A., “The Marshall-Olkin inverse Lomax distribution (MO-ILD) with application on cancer stem cell”, Journal of Advances in Mathematics and Computer Science, 33: 1–12, (2019).
• [14] Jones, M. C., “Families of distributions arising from distributions of order statistics”, TEST, 13 (1): 1-43, (2004).
• [15] Eugene, N., Lee C., Famoye, F., “Beta-normal distribution and its applications”, Communications in Statistics –Theory and Methods, 31: 497–512, (2002).
• [16] Alzaarteh, A., Lee, C., Famoye, F., “A new method for generating families of continuous distribution”, Merton, 71: 63-79, (2013).
• [17] AL-Shomrani, A., Arif, O., Shawky, A., Hanif, S., Shahbaz, M., Q., “Topp-Leone family of distributions: Some properties and applications”, Pakistan Journal of Statistics and Operation Research, 12(3): 443-451, (2016).
• [18] Rezaei, S., Sadr, B. B., Alizadeh, M., Nadarajah, S., “Topp–Leone generated family of distributions: Properties and applications”, Communication in Statistics-Theory and Methods, 46(6): 2893-2909, (2017).
• [19] Fisher, B., Kılıcman, A., “Some results on the gamma function for negative integers”, Applied Mathematics & Information Sciences, 6: 173-176, (2012).
• [20] Murthy, D. N. P., Xie, M., Jiang, R., “Weibull models”, 1st, John Wiley, New Jersey, (2004).
• [21] Jorgensen, B., “Statistical Properties of the Generalized Inverse Gaussian Distribution”, Springer-Verlag, New York, (1982).