On Pseudo Lindley distribution: properties and applications

In this paper, we give a treatment of the mathematical properties for a new distribution named a pseudo Lindley distribution (PsLD)[14]. The properties studied include: moments, cumulates, characteristic function, failure rate function, mean residual life function, Lorenz curve, stochastic ordering, asymptotic distribution of the extreme order statistics, maximum likelihood estimation and simulation schemes. An application to waiting time data at a bank is described.

Keywords:

Lindley distribution, gamma Lindley distribution,

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A. Asgharzadeh , H.S. Bakouch, L. Esmaeili (2013). Pareto Poisson-Lindley distribution and its application. Journal of Applied Statistics, pp. 1-18.
M. H. Gail and J. L.Gastwirth (1978). A scale-free goodness of fit test for the exponential distribution based on the Lorenz curve. Journal of the American Statistical Association 73 787–793.
M. E. Ghitany, B. Atieh, S. Nadarajah (2008a). Lindley distribution and its applications. Math. Comput. Simulation , 78, pp. 493-506 .
M.E. Ghitany, D.K. Al-Mutairi, S. Nadarajah (2008b). Zero-truncated Poisson–Lindley distribution and its application, Math. Comput. Simulation, 79, pp. 279–287.
J. F. Lawless (2003). Statistical models and methods for lifetime data. Wiley, New York.
M. R. Leadbetter, G. Lindgren, H. Rootzén (1987). Extremes and Related Properties of Random Sequences and Processes, Springer Verlag, New York.
D. V. Lindley (1958). Fiducial distributions and Bayes theorem. Journal of the Royal Society, series B, 20, pp. 102-107.
R. Shanker, S.Sharma, R.Shanker. (2013). A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics, vol. 4, pp. 363-368.
R. Shanker and A. Mishra (2013). A quasi Lindley distribution. African Journal of Mathematics and Computer Science Research,Vol. 6(4), pp. 64-71.
M. Sankaran (1970). The discrete Poisson-Lindley distribution. Biometrics, 26, pp. 145-149.
H. Zakerzadah, A. Dolati (2010). Generalized Lindley distribution. J. Math. Ext. 3(2), pp. 13-25.
H. Zeghdoudi, S. Nedjar (2016a). Gamma Lindley distribution and its application. Journal of Applied Probability and Statistics. Vol. 11, N ^∘ 1, 129-138.
H. Zeghdoudi, S. Nedjar (2016b). On Gamma Lindley distribution :proprieties and simulation. Journal of Computation and Applied Mathematics Probability and Statistics. 298, pp 167-174.
H. Zeghdoudi, S. Nedjar (2016c) A Pseudo Lindley distribution and its application.,J. Afrika Statistika. Vol 11 (1) page 923-932
H. Zeghdoudi, S. Nedjar (2017). A Poissson pseudo Lindley distribution and its application . Journal of Probability and Statistical Sciences. Vol. 15, No 1.