Abstract
In this paper, a new three-parameter lifetime model, called the new odd log-logistic Lindley (NOLL-L) distribution, is introduced. Some structural properties of the new distribution including ordinary and incomplete moments, quantile and generating functions and order statistics are obtained. The new density function can be expressed as a linear mixture of exponentiated Lindley densities. The different methods are discussed to estimate the model parameters and a simulation study is done to show the performance of the new distribution. The importance and flexibility of the new model are also illustrated empirically by means of two real data sets.
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Alizadeh, M., Ozel, G., Altun, E. and Abdi, M. (2017). The odd log-logistic Marshall-Olkin Lindley model for lifetime data. J. Stat. Theory Appl.16, 3, 382–400.
Altun, G., Alizadeh, M., Altun, E. and Ozel, G. (2017). Odd Burr Lindley distribution with properties and applications. Hacettepe J. Math. Stat.46, 2, 255–276.
Alzaatreh, A., Lee, C. and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron71, 1, 63–79.
Ashour, S.K. and Eltehiwy, M.A. (2015). Exponentiated power Lindley distribution. J. Adv. Res.24, 6, 895–905.
Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. J. Qual. Technol.27, 154–161.
Cordeiro, G.M., Ortega, E.M.M. and da Cunha, D.C.C. (2013). The exponentiated generalized class of distributions. J. Data Sci.11, 1–27.
Cordeiro, G.M., Alizadeh, M., Tahir, M.H., Mansoor, M., Bourguignon, M. and Hamedani, G.G. (2015). The beta odd log-logistic generalized family of distributions. Hacettepe J. Math. Stat.45, 73, 126–139.
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J. and Knuth, D.J. (1996). On the Lambert W function. Adv. Comput. Math.5, 1, 329–359.
Doornik, J.A. (2007). Object-oriented matrix programming using Ox, 3rd edn. Timberlake Consultants Press and Oxford, London.
Elbatal, I., Asgharzadeh, A. and Sharafi, F. (2015). A new class of generalized power Lindley distributions. J. Appl. Prob. Stat.10, 89–116.
Elbatal, I., Diab, L. and Elgarhy, M. (2016). Exponentiated Quasi Lindley Distribution. Int. J. Reliab. Appl.17, 1, 1–19.
Gross, A.J. and Clark, V.A. (1975). Survival distributions: Reliability applications in the biomedical sciences. Wiley, New York.
Ghitany, M.E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application. Math. Comput. Simul.78, 493–506.
Ghitany, M.E., Al-Mutairi, D.K., Balakrishhnan, N. and Al-Enezi, L.J. (2013). Power Lindley distribution and associated inference. Comput. Stat. Data Anal.64, 20–33.
Gradshteyn, I.S. and Ryzhik, I.M. (2000). Table of integrals, series and products. Academic Press, San Diego.
Jodrá, J. (2010). Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Math. Comput. Simul.81, 851–859.
Leadbetter, M.R., Lindgren, G. and Rootzéln, H. (1987). Extremes and related properties of random sequences and processes. Springer, New York.
Lindley, D.V. (1958). Fiducial distributions and Bayesian theorem. J. Royal Stat. Soc. B20, 102–107.
Merovci, F. (2013). Transmuted Lindley distribution. Int. J. Open Problems Comput. Sci. Math.6, 2, 63–72.
Merovci, F., Elbatal, I. and Puka, L. (2015). The McDonald quasi Lindley distribution and its applications. Acta Univ. Apulensis42, 87–105.
Nadarajah, S., Bakouch, H.S. and Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B73, 331–359.
Oluyede, B.O., Yang, T. and Makubate, B. (2016). A new class of generalized power Lindley distribution with application to lifetime data. Asian J. Math. Appl.6, 1–36.
Ozel, G., Alizadeh, M., Cakmakyapan, S., Hamedani, G., Ortega, E.M.M. and Cancho, G. (2017). The odd log-logistic Lindley Poisson model for lifetime data. Commun. Stat. Theory Methods46, 8, 6513–6537.
Pararai, M., Warahena-Liyanage, G. and Oluyede, B.O. (2017). Exponentiated power Lindley–Poisson distribution: Properties and applications. Commun. Stat. Theory Methods46, 10, 4726–4755.
Shanker, R. and Mishra, A. (2013). A quasi Lindley distribution. African J. Math. Comput. Sci. Res.6, 4, 64–71.
Sharma, V., Singh, S., Singh, U. and Aqiwal, V. (2015). The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data. J. Ind. Prod. Eng.32, 3, 162–173.
Sharma, V.K., Singh, S.K., Singh, U. and Merovci, F. (2016). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Commun. Stat. Theory Methods45, 19, 5709–5729.
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The authors would like to thank the anonymous referees for their useful comments and suggestions.
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Alizadeh, M., Altun, E., Ozel, G. et al. A New Odd Log-Logistic Lindley Distribution with Properties and Applications. Sankhya A 81, 323–346 (2019). https://doi.org/10.1007/s13171-018-0142-x
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DOI: https://doi.org/10.1007/s13171-018-0142-x