Parameter Estimation for Inverted Exponentiated Lomax Distribution with Right Censored Data

Year 2019, Volume: 32 Issue: 4, 1370 - 1386, 01.12.2019

Rokaya Elmorsy , Amal Hassan

https://doi.org/10.35378/gujs.452885

Cited By: 23

Abstract

A new three-parameter
lifetime model, called the inverted exponentiated Lomax (IEL)
distribution is proposed. The IEL distribution is the inverse form of the
exponentiated Lomax distribution. Some properties of the IEL distribution are
derived. The maximum likelihood and the asymptotic confidence interval
estimators are obtained in presence of Type I censored samples. Two real data
sets are used to illustrate the usefulness and flexibility of the IEL distribution
compared with some known distributions. 

Parameter Estimation for Inverted Exponentiated Lomax Distribution with Right Censored Data

Abstract

A new three-parameter
lifetime model, called the inverted exponentiated Lomax (IEL) distribution is
proposed. The IEL distribution is the inverse form of the exponentiated Lomax
distribution. Some properties of the IEL distribution are established. The maximum
likelihood and the asymptotic confidence interval estimators are obtained in
presence of Type I censored samples. Two real data sets are employed to clarify
the usefulness and flexibility of the IEL model with some known distributions. 

Keywords

Exponentiated Lomax distribution, Moments, Maximum likelihood, Type I Censoring

References

• [1] Abd-Elfattah, A. M. and Alharbey, H. A. “Estimation of Lomax parameters based on generalized probability weighted moments”. JKAU: Science, 22(2): 171-184, (2010).[2] Abd-Elfattah, A. M., Alaboud F. M. and Alharbey, H. A. “On sample size estimation for Lomax distribution”. Australian Journal of Basic and Applied Sciences, 1(4): 373-378, (2007).
• [3] Abdul-Moniem, I. B. and Abdel-Hameed, H. F. “On exponentiated Lomax distribution”. International Journal of Mathematical Education, 33(5): 1-7, (2012).[4] Ahsanullah, M. “Record values of the Lomax distribution”. Statistica Neerlandica, 45: 21–29, (1991).
• [5] Al-Zahrani, B. “An extended Poisson-Lomax distribution”. Advances in Mathematics: Scientific Journal, 4(2): 79-89, (2015).[6] Ashour S. K., Abdelfattah A. M., and Mohammad, B. S. K. “Parameter estimation of the hybrid censored Lomax distribution”. Pakistan Journal of Statistics and Operations Research, 7: 1–19, (2011).
• [7] Ashour, S. K., and Eltehiwy, M. A. “Transmuted exponentiated Lomax distribution”. Australian Journal of Basic and Applied Sciences, 7: 658–667, (2013).[8] Balakrishnan, N. and Ahsanullah, M. “Relations for single and product moments of record values from Lomax distribution”. Sankhya B, 56: 140-146, (1994).
• [9] Balkema, A. A. and de Hann, L. “Residual life time at great age”. The Annals of Probability, 2(5): 972–804, (1974).[10] Bryson, M. C. “Heavy-tailed distributions: properties and tests”. Technimetrics, 16: 61–68, (1974).
• [11] Childs, A., Balakrishnan, N. and Moshref, M. “Order statistics from non-identical right truncated Lomax random variables with applications”. Statistical Papers, 42(2): 187-206, (2001). [12] Popović, B. V., Cordeiro, G. M. and Ortega, E. “The gamma-Lomax distribution”. Journal of Statistical Computation and Simulation, 85(2): 305–319, (2013).
• [13] Dubey, S. “Compound gamma, beta and F distributions”. Metrika 16(1):27–31, (1970).[14] El-Bassiouny, A., Abdo N. and Shahen, H. “Exponential Lomax distribution”. International Journal of Computer Applications, 121(13):975–8887, (2015).
• [15] Fisher, B. and Kılıcman, A. “Some Results on the Gamma Function for Negative Integers”. Applied Mathematics and Information Sciences, 6: 173-176, (2012).[16] Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan, L. A. “Marshall-Olkin extended Lomax distribution and its application to censored data”. Communication in Statistics-Theory and Methods, 36(10): 1855-1866, (2007).
• [17] Gupta, R.C., Ghitany, M. E. and Al-Mutairi, D. K. “Estimation of reliability from Marshall-Olkin extended Lomax distributions”. Journal of Statistical Computation and Simulation, 80(8): 937–947, (2010). [18] Hassan A. S. and Al-Ghamdi, A. S. “Optimum step stress accelerated life testing for Lomax distribution”. Journal of Applied Sciences Research, 5(12):1-12, (2009).
• [19] Hassan, A. S. and Abd-Allah, M. “Exponentiated Weibull-Lomax distribution: properties and estimation”. Journal of Data Science, 16 (2): 277-298, (2018). [20] Hassan A. S. and Nassr S. G. “Power Lomax Poisson distribution: properties and estimation”. Journal of Data Science, 18(1):105-128, (2018).[21] Hassan, A. S., Assar, S. M. and Shelbaia, A. “Optimum step stress accelerated life test plan for Lomax distribution with an adaptive type-II progressive hybrid censoring”. British Journal of Mathematics and Computer Science, 13(2): 1-19, (2016).
• [22] Kenney, J. F. and Keeping, E. “Mathematics of Statistics”. D. Van Nostrand Company, (1962).[23] Lawless, J. F. “Statistical Models and Methods for Lifetime Data, Wiley, New York, (1982).
• [24] Lee, E. T. and Wang, J. W. “Statistical Methods for Survival Data Analysis”. 3rd edition, Wiley, New York, http://dx.doi.org/10.1002/0471458546, (2003).[25] Lemonte, A. J. and Cordeiro, G. M. “An extended Lomax distribution”. Statistics, 47(4):800–816, (2013).
• [26] Moors, J. J. A. “A quantile alternative for kurtosis”. Journal of the Royal Statistical Society. Series D (The Statistician), 37(1):25–32, (1988).[27] Myhre, J. and Saunders, S. “Screen testing and conditional probability of survival, In: Crowley, J. and Johnson, R.A., eds. Survival Analysis”. Lecture Notes-Monograph Series. Institute of Mathematical Statistics, 2: 166-178, (1982).
• [28] Rady, E. A., Hassanein, W. A. and Elhaddad, T. A. “The power Lomax distribution with an application to bladder cancer data”. Springer plus, 5:1838DOI 10.1186/s40064-016-3464-y, (2016).[29] Tahir, M. H., Cordeiro, G. M., Mansoor, M. and Zubair, M. “The Weibull-Lomax distribution: properties and applications”. Hacettepe Journal of Mathematics and Statistics, 44 (2): 461-480, (2015).
• [30] Tahir, M. H., Hussain, M. A., Cordeiro, G. M, Hamedani, G. G., Mansoor, M. and Zubair, M. “The Gumbel-Lomax distribution: properties and applications”. Journal of Statistical Theory and Applications, 15 (1): 61-79, (2016).