A new and unified approach in generalizing the  Lindley’s distribution with applications

Lahsen  Bouchahed; Halim  Zeghdoudi

doi:https://doi.org/10.21307/stattrans-2018-004

A new and unified approach in generalizing the Lindley’s distribution with applications

Lahsen Bouchahed LaPS laboratory, Badji-Mokhtar University, Box 12, Annaba, 23000, ALGERIA , Halim Zeghdoudi LaPS laboratory, Badji-Mokhtar University, Box 12, Annaba, 23000, ALGERIA Statistics in Transition new series, vol. 19, 2018, 1, pages: 61-74 Published online: 1 March 2018 https://doi.org/10.21307/stattrans-2018-004

223 Views 13 Downloads

ARTICLE

(English) PDF

ABSTRACT

This paper proposes a new family of continuous distributions with one extra shape parameter called the generalized Zeghdoudi distributions (GZD). We investigate the shapes of the density and hazard rate function. We derive explicit expressions for some of its mathematical quantities. Various statistical properties like stochastic ordering, moment method, maximum likelihood estimation, entropies and limiting distribution of extreme order statistics are established. We prove the flexibility of the new family by means of applications to several real data sets

KEYWORDS

Lindley distribution, exponential distribution, Gamma distribution, stochastic ordering, maximum-likelihood estimation.

REFERENCES

ASGHARZADEH, A., BAKOUCH, H, S., ESMAEILI, L., (2013). Pareto Poisson Lindley distribution and its application, Journal of Applied Statistics, pp. 1–18.

FULLER, E.J., FRIEMAN, S., QUINN, J., QUINN, G., CARTER, W. Fracture me chanics approach to the design of glass aircraft windows: A case study, SPIE Proc 2286, pp. 419–430 (1994).

GHITANY, M, E., AL-MUTAIRI, D, K., NADARAJAH, S., (2008a). Zero-truncated Poisson-Lindley distribution and its application, Math. Comput. Simulation,79, pp. 279–287.

GHITANY, M, E., ATIEH, B., NADARAJAH, S., (2008b). Lindley distribution and its applications. Mathematics and Computers in Simulation, 78, pp. 493–506.

GROSS, A,J., CLARK, V, A.,(1975). Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York.

LAURENS DE HAAN, FERREIRA, A., (2006). Extreme value theory: An introduc tion, Springer.

LAWLESS, J, F., (2003). Statistical models and methods for lifetime data, Wiley, New York.

LEADBETTER,M,R., LINDGREN, G., ROOTZén, H., (1987). Extremes and Re lated Properties of Random Sequences and Processes, Springer Verlag, New York.

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

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

SHANKER, R., SHARMA, S., SHANKER, R., (2013). A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics,Vol. 4, pp. 363–368.

SHANKER, R., (2015 a). Akash distribution and Its Applications. International Journal of Probability and Statistics, 4 (3), pp. 65–75.

SHANKER, R., (2015 b). Shanker distribution and Its Applications, International Journal of Statistics and Applications, 5 (6), pp. 338–348.

SHANKER, R., (2016 a). Aradhana distribution and Its Applications, International Journal of Statistics and Applications, 6 (1), pp. 23–34.

SHANKER, R., (2016 b). Sujatha distribution and Its Applications, Statistics in Transition new series, 17 (3), pp. 391–410.

SHANKER, R., (2016 c). Amarendra distribution and Its Applications, American Journal of Mathematics and Statistics, 6 (1), pp. 44–56.

SHANKER, R., (2016 d). Devya distribution and Its Applications, International Journal of Statistics and Applications, 6 (4), pp. 189–202.

SHANKER, R., (2016 e). Shambhu Distribution and Its Applications, International Journal of Probability and Statistics, 5 (2), pp. 48–63.

ZAKERZADAH, H., DOLATI, A., (2010). Generalized Lindley distribution, J. Math.Ext, 3(2), pp. 13–25.

ZEGHDOUDI, H., NEDJAR, S., (2016a). Gamma Lindley distribution and its appli cation, Journal of Applied Probability and Statistics, Vol. 11 (1), 129–138.

ZEGHDOUDI, H., NEDJAR, S., (2016b). On gamma Lindley distribution: Proper ties and Simulations, Journal of Computational and Applied Mathematics, Vol 298, pp 167–174.

ZEGHDOUDI, H., NEDJAR, S., (2016c). A pseudo Lindley distribution and its application, Journal Afrika Statistika, Vol. 11 (1), pp. 923–932.

ZEGHDOUDI, H., MESSADIA,H., (2018). Zeghdoudi Distribution and its Applica tions. International Journal of Computing Science and Mathematics, In Press