A three-parameter weighted Lindley  distribution and its applications to model survival time

Rama  Shanker; Kamlesh  Kumar Shukla; Amarendra  Mishra

doi:https://doi.org/10.59170/stattrans-2017-015

A three-parameter weighted Lindley distribution and its applications to model survival time

Rama Shanker Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea. , Kamlesh Kumar Shukla Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea. , Amarendra Mishra Department of Statistics, Patna University, Patna, India. Statistics in Transition new series, vol. 18, 2017, 2, pages: 291-310 Published online: 1 June 2017 https://doi.org/10.59170/stattrans-2017-015

197 Views 7 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this paper a three-parameter weighted Lindley distribution, including Lindley distribution introduced by Lindley (1958), a two-parameter gamma distribution, a two-parameter weighted Lindley distribution introduced by Ghitany et al. (2011) and exponential distribution as special cases, has been suggested for modelling lifetime data from engineering and biomedical sciences. The structural properties of the distribution including moments, coefficient of variation, skewness, kurtosis and index of dispersion have been derived and discussed. The reliability properties, including hazard rate function and mean residual life function, have been discussed. The estimation of its parameters has been discussed using the maximum likelihood method and the applications of the distribution have been explained through some survival time data of a group of patients suffering from head and neck cancer, and the fit has been compared with a one-parameter Lindley distribution and a two-parameter weighted Lindley distribution

KEYWORDS

moments, stochastic ordering, hazard rate function, mean residual life function, maximum likelihood estimation, lifetime data, goodness of fit.

REFERENCES

EFRON, B., (1988). Logistic regression, survival analysis and the Kaplan-Meier curve, Journal of the American Statistical Association, 83, pp. 414–425.

GHITANY, M. E., ATIEH, B., NADARAJAH. S., (2008). Lindley distribution and its Application, Mathematics Computing and Simulation, 78, pp. 493–506.

GHITANY, M. E., ALQALLAF, F., AL-MUTAIRI, D. K., HUSAIN, H. A.,(2011). A two-parameter weighted Lindley distribution and its applications to survival data, Mathematics and Computers in simulation, 81, pp. 1190–1201.

LINDLEY, D. V., (1958). Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society, Series B, 20, pp. 102–107.

SANKARAN, M., (1970). The discrete Poisson-Lindley distribution, Biometrics,26(1), pp. 145–149.

SHAKED, M., SHANTHIKUMAR, J. G., (1994). Stochastic Orders and Their Applications, Academic Press, New York.

SHANKER, R., MISHRA, A., (2013 a). A Two Parameter Lindley Distribution, Statistics in Transition new series, 14 (1), pp. 45–56.

SHANKER, R, MISHRA, A., (2013 b). A Quasi Lindley Distribution, African Journal of Mathematics and Computer Science Research (AJMCSR), 6 (4), pp. 64 – 71.

SHANKER, R., SHARMA, S., SHANKER, R., (2013). A Two Parameter Lindley Distribution for Modeling Waiting and Survival Times Data, Applied Mathematics, 4 (2), pp. 363–368.

SHANKER, R., AMANUEL, A. G., (2013). A New Quasi Lindley Distribution, International Journal of Statistics and System, 8 (2), pp. 143–156.

SHANKER, R., HAGOS, F., SUJATHA, S., (2015). On modeling of Lifetimes data using exponential and Lindley distributions, Biometrics & Biostatistics International Journal, 2 (5), pp. 1–9.

SHANKER, R., SHUKLA, K. K., HAGOS, F., (2016). On weighted Lindley distribution and Its applications to model Lifetime data, Jacobs Journal of Biostatistics, 1 (1), pp. 1–9