An extended life time distribution: theory, properties and applications

Year 2021, Volume: 50 Issue: 6, 1822 - 1837, 14.12.2021

Salman Abbas , Muhammad Mohsin

https://doi.org/10.15672/hujms.786853

Abstract

This paper is an addition to the series of modification and improvement of the extant distributions which enable them to analyze the new emerging situations efficiently. We develop a new lifetime distribution by generalizing the Erlang truncated exponential distribution using the Topp Leone family of distributions. A
comprehensive account of mathematical characteristics such as quantile function, moments, probability weighted moments, moment generating function, and probability generating function of the proposed
distribution is presented. Some reliability measures such as hazard rate function, residual life function, and reversed residual life function are also provided. Several entropy measures including Reyni entropy, Tsallis entropy, cumulative Tsallis entropy, and dynamic cumulative Tsallis entropy are obtained. Besides, the extropy, residual extropy, and cumulative residual extropy are explored. The unknown parameters of the proposed distribution are estimated by using the maximum likelihood method. The stability of the model parameters is examined through the simulation study. The application of our proposed distribution is explained through three real-life examples and its performance is illustrated through its comparison with the competent existing distributions.

Keywords

Erlang truncated exponential distribution, Topp Leone family of distributions, distributional characteristics, entropy, reliability measures, inferences

References

• [1] S. Abbas, S.A. Taqi, F. Mustafa, M. Murtaza and M.Q. Shahbaz, Topp-Leone inverse Weibull distribution: Theory and application, Eur. J. Appl. Math. 10 (5), 1005–1022, 2017.
• [2] S. Abu-Youssef, B. Mohammed and M. Sief, An extended exponentiated exponential distribution and its properties, Int. J. Comput. Appl. 121 (5), 1-6, 2015.
• [3] A.Z. Afify, M. Zayed, and M. Ahsanullah, The extended exponential distribution and its applications, J. Stat. Theory Appl. 17 (2), 213-229, 2018.
• [4] A. Al-Shomrani, O Arif, A. Shawky, S. Hanif and M.Q. Shahbaz, Topp–Leone family of distributions: Some properties and application, Pak. J. Stat. Oper. Res. 12 (3), 443-451, 2016.
• [5] J. Cartwright, Roll over, Boltzmann, Physics World 27 (05), 31-35, 2014.
• [6] S.T. Dara and M. Ahmad, Recent Advances in Moment Distribution and their Hazard Rates, LAP LAMBERT Academic Publishing, 2012.
• [7] A.R. El-Alosey, Random sum of new type of mixture of distribution, International Journal of Statistics and Systems 2 (1), 49-57, 2007.
• [8] M. Ghitany, D.K. Al-Mutairi, N. Balakrishnan and L. Al-Enezi, Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64, 20-33, 2013.
• [9] R.D. Gupta and D. Kundu, Theory & methods: Generalized exponential distributions, Aust. N. Z. J. Stat. 41 (2), 173-188, 1999.
• [10] D. Hinkley, On quick choice of power transformation J. R. Stat. Soc. Ser. C. Appl. Stat. 26 (1), 67-69, 1977.
• [11] S. Jahanshahi, H. Zarei and A. Khammar,On cumulative residual extropy, Probab. Engrg. Inform. Sci. 34 (4), 605-625, 2020.
• [12] A. Keller, A. Kamath and U. Perera, Reliability analysis of CNC machine tools, Reliab. Eng. 3 (6), 449-473, 1982.
• [13] M. Mohsin, M. Ahmad, S. Shahbaz and M.Q. Shahbaz, Concomitant of lower record for bivariate pseudo inverse rayleigh distribution, Sci.Int. (Lahore) 21 (1), 21-23, 2009.
• [14] M. Mohsin, S. Shahbaz and M.Q. Shahbaz, A characterization of Erlang-truncated exponential distribution in record values and its use in mean residual life, Pak. J. Stat. Oper. Res. 6 (2), 143-148, 2010.
• [15] S. Mol, O. Ozden and S. Karakulak, Levels of selected metals in albacore (Thunnus alalunga, Bonnaterre, 1788) from the Eastern Mediterranean, J. Aquat. Food Prod. Technol. 21 (2), 111-117, 2012.
• [16] S. Nadarajah and S. Kotz, Moments of some J-shaped distributions, J. Appl. Stat. 30 (3), 311-317, 2003.
• [17] S. Nadarajahand and S. Kotz, The beta exponential distribution, Reliab. Eng. Syst. Saf. 91 (6), 689-697, 2006.
• [18] S. Nasiru, M. Atem and K. Nantomah, Poisson exponentiated Erlang-truncated exponential distribution, J. Stat. Appl. Probab. 7 (2), 245-261, 2018.
• [19] S. Nasiru, A. Luguterah and M.M. Iddrisu, Generalized Erlang-truncated exponential distribution, Advances and Applications in Statistics 48 (4), 273-301, 2016.
• [20] I.E. Okorie, C.A. Akpanta and J. Ohakwe, Transmuted Erlang-truncated exponential distribution, Econ. Qual. Control 31 (2), 71-84, 2016.
• [21] I.E. Okorie, A. Akpanta and J. Ohakwe, Marshall-Olkin generalized Erlang-truncated exponential distribution: Properties and applications, Cogent Math. 4 (1), 1285093, 2017.
• [22] I.E. Okorie, A. Akpanta, J. Ohakwe and D. Chikezie, The extended Erlang-truncated exponential distribution: Properties and application to rainfall data, Heliyon 3 (6), e00296, 2017.
• [23] A. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integrals and Series, More Special Functions, CRC Press, 1986.
• [24] G. Qiu and K. Jia, The residual extropy of order statistics, Statist. Probab. Lett. 133, 15-22, 2018.
• [25] A. Renyi, On measures of entropy and information, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Contributions to the Theory of Statistics, The Regents of the University of California, 1961.
• [26] M.M. Sati and N. Gupta, Some characterization results on dynamic cumulative residual tsallis entropy, J. Probab. Stat., Doi:10.1155/2015/694203, 2015.
• [27] C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1-2), 479-487, 1988.