Submit Manuscript | http://medcraveonline.com Introduction The Lindley distribution introduced by Lindley et al., 2 in the context of Bayesian analysis as a counter example of fducial statistics, is defned by its probability density function (PDF) and cumulative distribution function (CDF) as ( ) 1 1 1 θ θ θ −   = − +   +   x x Gx e (1.1) And ( ) ( ) 2 x gx 1 x 1 e θ θ θ − = + + (1.2) respectively. For x 0, 0, θ > > where θ is the scale parameter of the Lindley distribution. Details of this distribution, its mathematical and statistical properties, estimation of its parameter and application including the superiority of Lindley distribution over exponential distribution has been done by Ghitany et al., 3 We have so many generalized families of distributions proposed by different researchers that are used in extending other distributions to produce compound distributions with better performance. These are several ways of adding one or more parameters to a distribution function which makes the resulting distribution richer and more fexible for modeling data. A brief summary of some of these methods or families of distribution include the beta generalized family (Beta-G) by Eugene et al., 4 the Kumaraswamy-G by Cordeiro et al. 5 Transmuted family of distributions by Shaw et al., 6 Gamma-G (type 1) by Zografos et al., 7 McDonald-G by Alexander et al., 8 Gamma-G (type 2) by Risti et al., 9 Gamma-G (type 3) by Torabi et al., 10 Log-gamma-G by Amini et al., 9 Exponentiated T-X by Alzaghal et al., 12 Exponentiated-G (EG) by Cordeiro et al., 13 Logistic-G by Torabi et al., 14 Gamma-X by Alzaatreh et al., 15 Logistic-X by Tahir et al., 16 Weibull-X by Alzaatreh et al., 17 Weibull-G by Bourguignon et al., 18 a new Weibull-G family by Tahir et al., 1 a Lomax-G family by Cordeiro et al., 19 a new generalized Weibull-G family by Cordeiro et al., 20 and Beta Marshall-Olkin family of distributions by Alizadeh et al., 21 and some other families of the distributions. Hence, there are also some generalizations of the Lindley distribution recently proposed in the literature such as the transmuted Lindley distribution by Merovci et al., 23 the exponentiated Power Lindley distribution by Ashour et al., 24 Generalized Lindley distribution by Nadarajah et al., 24 Transmuted Generalized Lindley distribution by Elgarhy et al., 25 Extended Power Lindley distribution by Alkarni et al., 26 a two-parameter Lindley distribution by Shanker et al., 27 the Lomax-Lindley distribution by Yahaya et al., 28 Transmuted Two-Parameter Lindley distribution by Al-khazaleh et al., 29 and a three-parameter Lindley distribution by Shanker et al., 30 The aim of this article is to introduce a new continuous distribution called Weibull-Lindley distribution (WLnD) from the proposed family by Tahir et al., 1 The remaining parts of this article are presented in sections as follows: We defned the new distribution and give its plots in section 2.1. Section 2.2 derived some properties of the new distribution. Section 2.3 proposes some reliability functions of the new distribution. The order statistics for the new distribution are also given in section 2.4. The maximum likelihood estimates (MLEs) of the unknown model parameters of the new distribution are obtained in section 2.5. In section 3 we carryout application of the proposed model with others to four lifetime datasets. Lastly, in section 4, we give the summary of our work and concluding remarks. Materials and methods Construction of Weibull-Lindley distribution (WLnD) In the next section, we have defned the cdf and pdf of the Weibull- Lindley distribution (WLnD) using the method proposed by Tahir et al. 1 According to Tahir et al., 1 the formula or Weibull link function for deriving the cdf and pdf of any Weibull-based continuous distribution is defned as: { } log G(x) t log G(x) 1 0 F(x) t dt e e β β α α β αβ −     − − −   −   = = ∫ (2.1.1) And { } { } 1 log G(x) g(x) f(x) log G(x) G(x) e β β α αβ − − −     = −     (2.1.2) respectively, where ( ) gx and ( ) Gx are the pdf and cdf of any continuous distribution to be generalized respectively and α and β are the two additional new parameters responsible for the shape of the distribution. Biom Biostat Int J. 2018;7(6):532‒544. 532 © 2018 Ieren et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially. Modeling lifetime data with Weibull-Lindley distribution Volume 7 Issue 6 - 2018 Ieren TG, Oyamakin SO, Chukwu AU Department of Statistics, University of Ibadan, Nigeria Correspondence: Ieren TG, Department of Statistics, University of Ibadan, Ibadan, Nigeria, Email Received: October 15, 2018 | Published: November 23, 2018 Abstract In this paper a new extension of the Lindley distribution is presented using the Weibull link function introduced and studied by Tahir et al., 1 to develop a Weibull-Lindley distribution. We derive and discuss the mathematical and Statistical properties of the subject distribution along with its reliability analysis and inference for the parameters. Finally, the Weibull- Lindley distribution has been used to model four lifetime datasets and the results show that the proposed generalization performs better than the other known extensions of the Lindley distribution considered for the study.. Keywords: Lindley distribution, Weibull-Lindley distribution, mathematical properties, reliability function, parameter estimation, applications. Biometrics & Biostatistics International Journal Research Article Open Access