The study describes the general concept of the XLindley distribution. Forms of density and hazard rate functions are investigated. Moreover, precise formulations for several numerical properties of distributions are derived. Extreme order statistics are established using stochastic ordering, the moment method, the maximum likelihood estimation, entropies and the limiting distribution. We demonstrate the new family's adaptability by applying it to a variety of real-world datasets.
exponential distribution, Xgamma distribution, Lindley distribution, quantile function stochastic ordering, maximum-likelihood estimation, XLindley distribution
Akaike, H., (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC-19, pp. 716–723.
Asgharzadeh, A., Hassan, S. and Bakouch, L. E., (2013). Pareto Poisson-Lindley distribution and its application. Journal of Applied Statistics, Vol. 40, No. 8, pp. 1–18.
Bashir, S., Rasul, M., (2015). Some properties of the weighted Lindley distribution. International Journal of Economic and Business Review, 3 (8), pp. 11–17.
Beghriche, A. F., Zeghdoudi, H., (2019). A Size Biased Gamma Lindley Distribution. Thailand Statistician, Vol.17, No 2, pp. 179–189.
Fisher, R. A., (1934). The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, , 6, pp. 13–25.
Ghitany, M. E, Atieh, B and Nadarajah, S., (2008b). Lindley distribution and its applications. Mathematics and Computers in Simulation, 78, pp. 493–506.
Glaser, R. E., (1980). Bathtub and related failure rate characterizations. J. Amer.Statist. Assoc., 75, pp. 667–672.
Gupta R. D., Kundu D., (1999). Generalized Exponential distribution. Australian and New Zealand Journal of Statistics, Vol. 41, No. 2, pp.173–188.
Laurens de Haan, Ferreira A., (2006). Extreme value theory: An introduction. Springer.
Lawless, J. F., (2003). Statistical models and methods for lifetime data. Wiley, New Y  Sen, Subhradev; Maiti, Sudhansu S.; and Chandra, N., (2016). The Xgamma Distribution: Statistical Properties and Application. Journal of Modern Applied Statistical Methods, Vol. 15, Iss. 1, Article 38.
Lindley, D. V., (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Society, series B, 20, pp. 102–107.
Patil, G. P., Rao, C. R., (1977). Weighted distribution survey of their applications, In P. R. Krishnaiah, (E ds.), Applications of statistics, pp. 383–405, Amsterdam, North Holland.
Patil, G. P., Rao, C. R., (1978). Weighted distributions and size biased sampling with applications to wild life populations and human families. Biometrics, 34, pp. 179–189.
Sen Subhradev, Maiti Sudhansu S. and Chandra, N., (2016). The xgamma Distribution: Statistical Properties and Application. Journal of Modern Applied Statistical Methods, Vol. 15, Iss. 1, Article 38. DOI: 10.22237/jmasm/1462077420.
Zeghdoudi, H., Bouchahed, L., (2018). A new and unified approach in generalizing the Lindley’s distribution with applications. Statistics in Transition new series, Vol. 19, No. 1, pp. 61–74,
Zeghdoudi, H., Messadia, M., (2018). Zeghdoudi Distribution and its Applications. International Journal of Computing Science and Mathematics, Vol. 9, No.1, pp. 58–65.
Zeghdoudi, H.,. Nedjar, S., (2016c). A pseudo Lindley distribution and its application. Afr. Stat., Vol. 11, No. 1, pp. 923–932.