A Lomax-inverse Lindley Distribution: Model, Properties and Applications to Lifetime Data

Main Article Content

Terna Godfrey Ieren
Peter Oluwaseun Koleoso
Adana’a Felix Chama
Innocent Boyle Eraikhuemen
Nasiru Yakubu

Abstract

This article proposed a new extension of the Inverse Lindley distribution called “Lomax-Inverse Lindley distribution” which is more flexible compared to the Inverse Lindley distribution and other similar models. The paper derives and discusses some Statistical properties of the new distribution which include the limiting behavior, quantile function, reliability functions and distribution of order statistics. The parameters of the new model are estimated by method of maximum likelihood estimation. Conclusively, three lifetime datasets were used to evaluate the usefulness of the proposed model and the results indicate that the proposed extension is more flexible and performs better than the other distributions considered in this study.

Keywords:
Inverse lindley distribution, lomax-inverse lindley distribution, statistical properties, order statistics, parameter estimation, applications.

Article Details

How to Cite
Ieren, T. G., Koleoso, P. O., Chama, A. F., Eraikhuemen, I. B., & Yakubu, N. (2019). A Lomax-inverse Lindley Distribution: Model, Properties and Applications to Lifetime Data. Journal of Advances in Mathematics and Computer Science, 34(3-4), 1-28. https://doi.org/10.9734/jamcs/2019/v34i3-430208
Section
Original Research Article

References

Lindley DV. Fiducial distributions and Bayes Theorem. J. Roy. Stat. Soc. Series B (Methodological). 1958;102–107.

Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math. Comput. Simul. 2008;78(4);493–506.

Mazucheli J, Achcar JA. The lindley distribution applied to competing risks lifetime data. Comput. Methods Programs Biomed. 2011;104:188–192.

Krishna H, Kumar K. Reliability estimation in Lindley distribution with progressively type-ii right censored sample. Math. Comput. Simul. 2011;82:281–294.

Singh B, Gupta PK. Load-sharing system model and its application to the real data set. Math. Comput. Simul. 2012;82:1615–1629.

Al-Mutairi DK, Ghitany ME, Kundu D. Inferences on stress-strength reliability from Lindley distributions. Commun. Stat. - Theory and Methods. 2013;42;1443–1463.

Sharma VK, Singh SK, Singh U. A new upside-down bathtub shaped hazard rate model for survival data analysis. Appl. Math. Comput. 2014;239:242–253.

Zakerzadeh H, Dolati A. A generalised Lindley distribution. J. Math Extension. 2009;3:13-25.

Nadarajah S, Bakouch H, Tahmasbi R. A generalized Lindley distribution. Sankhya B-Applied and Interdisc. Stat. 2011;73:331–359.

Ghitany M, Al-Mutairi D, Balakrishnan N, Al-Enezi L. Power Lindley distribution and associated inference. Comput. Stat. Data Anal. 2013;64:20–33.

Merovci F. Transmuted Lindley distribution. Int. J. Open Prob. Computer Sci. Math. 2013;6: 63–72.

Merovci F, Elbatal I. Transmuted Lindley-geometric distribution and its applications. J. Stat. Appl. Probability Lett. 2014;3:77–91.

Merovci F, Sharma VK. The beta Lindley distribution: properties and applications. J. Appl. Math. 2014;1–10.

Elbatal I, Elgarhy M. Statistical properties of Kumaraswamy quasi Lindley distribution. Int. J. Math. Trends Technol. 2013;4:237–246.

Akmakyapan S, Kadlar GZ. A new customer lifetime duration distribution: The Kumaraswamy Lindley distribution. Int. J. Trade, Economics Finance. 2014;5:441–444.

Ashour SK, Eltehiwy MA. Exponentiated power Lindley distribution. J. Adv. Res. 2015;6: 895–905.

Ramos PL, Louzada F. The generalized weighted Lindley distribution: Properties, estimation, and applications. Cogent Math. 2016;3(1):1256022.

Sharma VK, Singh SK, Singh U, Agiwal V. The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. J. Indust. Prod. Eng. 2015;32(3):162–173.

Sharma VK, Singh SK, Singh U, Merovci F. The generalized inverse Lindley distribution: a new inverse statistical model for the study of upside down bathtub data. Commun. Stat.-Theo. Meth. 2016;45(19):5709–5729.

Alkarni SH. Extended inverse Lindley distribution: Properties and application. Springer- Plus. 2015;4:1–13.

Ramos PL, Louzada F, Shimizu TK, Luiz AO. The inverse weighted Lindley distribution: Properties, estimation and an application on a failure time data. Communications in Statistics-Theory and Methods. 2019;48(10);2372-2389.

Gomes-Silva F, Percontini A, De Brito E, Ramos MW, Venancio R, Cordeiro GM. The odd Lindley-G family of distributions. Austrian J. of Stat. 2017;46:65-87.

Cakmakyapan S, Ozel G. The Lindley family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics. 2016;46:1-27,
DOI: 10.15672/hjms.201611615850

Tahir MH, Zubair M, Mansoor M, Cordeiro GM, Alizadeh M. A new Weibull-G family of distributions. Hac. J. Math. Stat., 2016;45(2):629-647.

Cordeiro GM, Ortega EMM, Popovic BV, Pescim RR. The Lomax generator of distributions: Properties, minification process and regression model. Appl. Math. Comp., 2014;247:465-486.

Ieren TG, Kuhe AD. On the properties and applications of Lomax-Exponential distribution. Asian J. Prob. Stat. 2018;1(4):1-13.

Omale A, Yahaya A, Asiribo OE. On properties and applications of Lomax-Gompertz distribution. Asian J. Prob. Stat. 2019;3(2):1-17.

Venegas O, Iriarte YA, Astorga JM, Gomez HW, Lomax-Rayleigh distribution with an application. Appl. Math. Inf. Sci., 2019;13(5):741-748.

Ieren TG, Oyamakin SO, Yahaya A, Chukwu AU, Umar AA, Kuje S. On making an informed choice between two Lomax-Based continuous probability distributions using lifetime data. Asian J. Prob. Stat. 2018;2(2):1-11.

Hyndman RJ, Fan Y. Sample quantiles in statistical packages, The American Stat. 1996;50 (4):361-365.

Kenney JF, Keeping ES. Mathematics of Statistics, 3 edn, Chapman & Hall Ltd, New Jersey; 1962.

Moors JJ. A quantile alternative for kurtosis. J. of the Royal Stat. Society: Series D. 1988; 37:25–32.

Chen G, Balakrishnan N. A general purpose approximate goodness-of-fit test. Journal of Quality Technology. 1995;27:154–161.

Core Team R. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2019.
Avaiable: https://www.R-project.org/

Gross AJ, Clark VA. Survival distributions reliability applications in the Biometrical Sciences. John Wiley, New York, USA; 1975.

Shanker R, Fesshaye H, Sharma S. On two-Parameter Lindley distribution and its applications to model lifetime data. Biom. Biostat. Int. J. 2016;3(1):00056.
DOI: 10.15406/bbij.2016.03.00056

Ieren TG, Oyamakin SO, Chukwu AU. Modeling lifetime data with Weibull-Lindley distribution. Biomet. Biostat. Int. J. 2018;7(6):532‒544.

Afify AZ, Aryal G. The Kummaraswamy exponentiated Frechet distribution. Journal of Data Science. 2016;6:1-19.

Barreto-Souza WM, Cordeiro GM, Simas AB. Some results for beta Frechet distribution. Comm. Stat.: Theo and Meths. 2011;40:798-811.

Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G family of probability distributions, J. Data Sci. 2014;12:53-68.

Oguntunde PE, Balogun OS, Okagbue HI, Bishop SA, The Weibull-Exponential Distribution: Its properties and applications. J. Appl. Sci. 2015;15(11):1305-1311.

Ieren TG, Yahaya A. The Weimal distribution: Its properties and applications. J. Nigeria Ass. Math. Physics. 2017;39:135-148.

Smith RL, Naylor JC. A comparison of maximum likelihood and bayesian estimators for the Three-Parameter Weibull distribution. J. of Appl. Stat. 1987;36:358-369.

Balakrishnan N, Leiva V, Sanhueza A, Cabrera E. Mixture inverse Gaussian distributions and its transformations, moments and applications. Stat. 2009;43;91–104.