A Three Parameter Generalized Lindley Distribution: Properties and Application
Keywords:Lindley distribution, Power Lindley distribution, Hazard rate, Moments
In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study.
A. AL-BABTAIN, A. M. EID, A. N. AHMED, F. MEROVCI (2015). The five parameter Lindley distribution. Pakistan Journal of Statistics, 31, no. 4, pp. 363-384.
A. ALZAARTREH, C. LEE, F. FAMOYE (2013). A new method for generating families of continuous distributions. Metron, 71, no. 1, pp. 63-79.
A. AKINSETE, F. FAMOYE, C. LEE (2008). The beta-Pareto distribution. Statistics, 42, pp. 547-563.
H. BAKOUCH, B. AL-ZAHRANI, A. AL-SHOMRANI, V.MARCHI, F. LOUZAD (2012). An extended Lindley distribution. Journal of the Korean Statistical Society, 41, pp. 75-85.
W. T. BERA (2015).The Kumaraswamy Inverse Weibull Poisson Distribution with Applications. Theses and Dissertations, 1287. Indiana University of Pennsylvania. http://knowledge.library.iup.edu/etd/1287
D. BHATI, M. A. MALIK, H. J. VAMAN (2015). Lindley-exponential distribution: Properties and applications. Metron, 73, no. 3, pp. 335-357.
V. CHOULAKIAN, M. A. STEPHENS (2001). Goodness-of-fit for the generalized Pareto distribution. Technometrics, 43, no.4, pp. 478-484.
M. GHITANY, B. ATIEH, S. NADADRAJAH (2008). Lindley distribution and its applications. Mathematics and Computers in Simulation, 78, pp. 493-506.
M.GHITANY, D.AL-MUTAIRI,N. BALAKRISHNAN, I.AL-ENEZI (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, pp. 20-33.
P. JODRA (2010). Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function. Mathematical Computations and Simulation, 81, pp. 851-859.
N. LAZRI, H. ZEGHDOUDI (2016). On Lindley-Pareto Distribution: Properties and Application. Journal of Mathematics, Statistics and Operations Research, 3, no.2, pp. 1-7.
D. V. LINDLEY (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society, Series B, 20, no. 1, pp. 102-107.
R. MAYA, M. R. IRSHAD (2017). New extended generalized Lindley distribution: Properties and applications. Statistica, 77, no. 1, pp. 33-52.
S. NADARAJAH, H. BAKOUCH, R. TAHMASBI (2011). A generalized Lindley distribution. Sankhya B: Applied and Interdisciplinary Statistics, 73, pp. 331-359.
A. RÉNYI (1961). On measure of entropy and information. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, pp. 547-561.
R. SHANKER, S. SHARMA, U. SHANKER, R. SHANKER (2013). Sushila distribution and its application to waiting times data. International Journal of Business Management, 3, no. 2, pp. 1-11.
F. G. SILVA, A. PERCONTINI, E. BRITO, M. V. RAMOS, R. VENANCIO, G. CORDEIRO (2017). The odd Lindley-G family of distributions. Austrian Journal of Statistics, 46, pp. 65-87.
R. L. SMITH, J. NAYLOR (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, pp. 358-369.
G. WARAHENA-LIYANAGE, M. PERARAI (2014). A Generalized Power Lindley Distribution with Applications. Asian Journal of Mathematics and Applications (article ID ama0169), pp. 1-23.
M. WANG (2013). A new three-parameter lifetime distribution and associated inference, arXiv:1308.4128v1.