A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data

Affiliation(s)

Department of Statistics, Eritrea Institute of Technology, Mainefhi, Eritrea.

Department of Mathematics, Dayalbagh Educational Institute, Agra, India.

Department of Mathematics, G.L.A. College, N.P. University, Daltonganj, India.

Department of Statistics, Eritrea Institute of Technology, Mainefhi, Eritrea.

Department of Mathematics, Dayalbagh Educational Institute, Agra, India.

Department of Mathematics, G.L.A. College, N.P. University, Daltonganj, India.

ABSTRACT

In this paper, a two-parameter Lindley distribution, of which the one parameter Lindley distribution (LD) is a particular case, for modeling waiting and survival times data has been introduced. Its moments, failure rate function, mean residual life function, and stochastic orderings have been discussed. It is found that the expressions for failure rate function mean residual life function and stochastic orderings of the two-parameter LD shows flexibility over one-parameter LD and exponential distribution. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets relating to waiting times and survival times to test its goodness of fit to which earlier the one parameter LD has been fitted by others and it is found that to almost all these data-sets the two parameter LD distribution provides closer fits than those by the one parameter LD.

Cite this paper

R. Shanker, S. Sharma and R. Shanker, "A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data,"*Applied Mathematics*, Vol. 4 No. 2, 2013, pp. 363-368. doi: 10.4236/am.2013.42056.

R. Shanker, S. Sharma and R. Shanker, "A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data,"

References

[1] D. V. Lindley, “Fiducial Distributions and Bayes’ Theorem,” Journal of the Royal Statistical Society, Series B, Vol. 20, No. 1, 1958, pp. 102-107.

[2] D. V. Lindley, “Introduction to Probability and Statistics from Bayesian Viewpoint,” Cambridge University Press, New York, 1965. doi:10.1017/CBO9780511662973

[3] M. E. Ghitany, B. Atieh and S. Nadarajah, “Lindley Distribution and Its Applications,” Mathematics and Computers in Simulation, Vol.78, No. 4, 2008, pp. 493-506. doi:10.1016/j.matcom.2007.06.007

[4] E. G. Deniz and E. C. Ojeda, “The Discrete Lindley Distribution-Properties and Applications,” Journal of Statistical Computation and Simulation, Vol. 81, No. 11, 2011, pp. 1405-1416. doi:10.1080/00949655.2010.487825

[5] M. Sankaran, “The Discrete Poisson-Lindley distribution,” Biometrics, Vol. 26, No. 1, 1970. pp. 145-149. doi:10.2307/2529053

[6] J. Mazucheli and J. A. Achcar, “The Lindley Distribution Applied to Competing Risks Lifetime Data,” Computer Methods and Programs in Biomedicine, Vol. 104, No. 2, 2011, pp. 188-192. doi:10.1016/j.cmpb.2011.03.006

[7] M. E. Ghitany, F. Alqallaf, D. K. Al-Mutairi and H. A. Hussain, “A Two Parameter Weighted Lindley Distribution and Its Applications to Survival Data,” Mathematics and Computers in Simulation, Vol. 81, No. 6, 2011, pp. 1190-1201. doi:10.1016/j.matcom.2010.11.005

[8] H. S. Bakouch, B. M. Al-Zahrani, A. A. Al-Shomrani, V. A. A. Marchi and F. Louzada, “An Extended Lindley Distribution,” Journal of the Korean Statistical Society, Vol. 41, No. 1, 2012, pp. 75-85. doi:10.1016/j.jkss.2011.06.002

[9] T. Bjerkedal, “Acquisition of Resistance in Guinea Pigs Infected with Different Doses of Virulent Tubercle Bacilli,” American Journal of Epidemiology, Vol. 72, No. 1, 1960, pp. 130-148.

[10] S. Paranjpe and M. B. Rajarshi, “Modeling Non-Monotonic Survivorship Data with Bath Tube Distributions,” Ecology, Vol. 67, No. 6, 1986, pp. 1693-1695. doi:10.2307/1939102

[1] D. V. Lindley, “Fiducial Distributions and Bayes’ Theorem,” Journal of the Royal Statistical Society, Series B, Vol. 20, No. 1, 1958, pp. 102-107.

[2] D. V. Lindley, “Introduction to Probability and Statistics from Bayesian Viewpoint,” Cambridge University Press, New York, 1965. doi:10.1017/CBO9780511662973

[3] M. E. Ghitany, B. Atieh and S. Nadarajah, “Lindley Distribution and Its Applications,” Mathematics and Computers in Simulation, Vol.78, No. 4, 2008, pp. 493-506. doi:10.1016/j.matcom.2007.06.007

[4] E. G. Deniz and E. C. Ojeda, “The Discrete Lindley Distribution-Properties and Applications,” Journal of Statistical Computation and Simulation, Vol. 81, No. 11, 2011, pp. 1405-1416. doi:10.1080/00949655.2010.487825

[5] M. Sankaran, “The Discrete Poisson-Lindley distribution,” Biometrics, Vol. 26, No. 1, 1970. pp. 145-149. doi:10.2307/2529053

[6] J. Mazucheli and J. A. Achcar, “The Lindley Distribution Applied to Competing Risks Lifetime Data,” Computer Methods and Programs in Biomedicine, Vol. 104, No. 2, 2011, pp. 188-192. doi:10.1016/j.cmpb.2011.03.006

[7] M. E. Ghitany, F. Alqallaf, D. K. Al-Mutairi and H. A. Hussain, “A Two Parameter Weighted Lindley Distribution and Its Applications to Survival Data,” Mathematics and Computers in Simulation, Vol. 81, No. 6, 2011, pp. 1190-1201. doi:10.1016/j.matcom.2010.11.005

[8] H. S. Bakouch, B. M. Al-Zahrani, A. A. Al-Shomrani, V. A. A. Marchi and F. Louzada, “An Extended Lindley Distribution,” Journal of the Korean Statistical Society, Vol. 41, No. 1, 2012, pp. 75-85. doi:10.1016/j.jkss.2011.06.002

[9] T. Bjerkedal, “Acquisition of Resistance in Guinea Pigs Infected with Different Doses of Virulent Tubercle Bacilli,” American Journal of Epidemiology, Vol. 72, No. 1, 1960, pp. 130-148.

[10] S. Paranjpe and M. B. Rajarshi, “Modeling Non-Monotonic Survivorship Data with Bath Tube Distributions,” Ecology, Vol. 67, No. 6, 1986, pp. 1693-1695. doi:10.2307/1939102