On the characterisation of X-Lindley distribution by truncated moments. Properties and application

• Autorzy: Metiri Farouk , Zeghdoudi Halim , Ezzebsa Abdelali

Identyfikatory

DOI

10.37190/ord220105

• Języki publikacji: EN

Abstrakty

EN

Several papers introduce the new distributions and their applications, including, among others, those of Ducey and Gove [7], Grine and Zeghdoudi [8], Chouia et al. [5], Seghier et al. [11], Beghriche and Zeghdoudi [4], where characterisation of a probability distribution plays an important role in statistical science. Several researchers studied the characterisations of probability distributions. For example, Su and Huang [12] study the characterisations of distributions based on expectations. In addition, Nanda [10] studies the characterisations by average residual life and the failure rates of functions of absolutely continuous random variables. Ahmadi et al. [1] consider the estimation based on the left-truncated and right randomly censored data arising from a general family of distributions. On the other hand, Ahsanullah et al. [2, 3] present two characterisations of Lindley distribution, standard normal distribution, t-Student’s, exponentiated exponential, power function, Pareto, and Weibull distributions based on the relation of failure rate, reverse failure rate functions with left and right truncated moments. Recently, Haseeb and Yahia [9] studied truncated moments for two general classes of continuous distributions. In this paper, two characterisations of the X-Lindley distribution, introduced by Chouia and Zeghdoudi [5] have been studied. They are based on the failure, relation of the inverse failure rate functions with the left and right truncated moments, respectively. Section 2 gives some properties of X-Lindley distribution. Section 3 discusses the characterisation of general distribution by left truncated and failure rate function and then right truncated and reverse failure rate function. Section 4 studies the characterisation of X-Lindley distribution by using the relation between left/right truncated moment and failure/reverse failure rate function. Finally, an illustrative example of X-Lindley distribution with other one-parameter distributions is given to show the superiority and flexibility of this model.

Słowa kluczowe

EN

Lindley distribution; X-Lindley distribution; truncated moment; failure rate function; reversed failure rate function; characterisation of distributions

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2022
• Tom: Vol. 32, No. 1
• Strony: 99--109
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Metiri Farouk

• LaPS laboratory, Badji-Mokhtar University, Box 12, Annaba, 23000 Algeria

autor

Zeghdoudi Halim

• Department of Mathematics, University May 8, 1945-Guelma, Algeria

autor

Ezzebsa Abdelali

• Department of Mathematics, University May 8, 1945-Guelma, Algeria

Bibliografia

• [1] AHMADI J., DOOSTPARAST M., PARSIAN A., Estimation with left-truncated and right censored data: A comparison study, Stat. Prob. Lett., 2012, 82, 1391–1400.
• [2] AHSANULLAH M., GHITANY M.E., AL-MUTAIRI D.K., Characterisation of Lindley distribution by truncated moments, Comm. Stat. Theor. Meth., 2017, 46 (12), 6222–6227.
• [3] AHSANULLAH M., SHAKIL M., GOLAM KIBRIA B.M., Characterisations of continuous distributions by Truncated Moment, J. Mod. Appl. Stat. Meth., 2016, 15 (1), 316–331, DOI: 10.22237/jmasm/1462076160.
• [4] BEGHRICHE A., ZEGHDOUDI H., A size biased gamma Lindley distribution, Thail. Stat., 2019, 17 (2),179–189.
• [5] CHOUIA S., ZEGHDOUDI H., The X-Lindley distribution: Properties and application, J. Stat. Theor. Appl., 2021, 20 (2), 318–327.
• [6] CHOUIA S., ZEGHDOUDI H., RAMAN V., BEGHRICHE A., A new size biased distribution with application, J. Appl. Prob. Stat., 2021, 16 (1), 111–125.
• [7] DUCEY M.J., GOVE J.H., Size-biased distributions in the generalized beta distribution family with applications to forestry, Forestry, 2015, 88, 143–151, DOI: 10.1093/forestry/cpu038.
• [8] GRINE R., ZEGHDOUDI H., On Poisson quasi-Lindley distribution and its applications, J. Mod. Appl. Stat. Meth., 2017, 16 (2), 403–417, DOI. 10.22237/jmasm/1509495660.
• [9] HASEEB A., YAHIA A.A., Characterisation of general class of distributions by truncated moment,Thail. Stat., 2020, 18 (2), 95–107.
• [10] NANDA A.K., Characterisations of distributions through failure rate and mean residual life function, Stat. Prob. Lett., 2010, 80, 752–755.
• [11] SEGHIER F.Z., ZEGHDOUDI H., BENCHAABANE A., A size-biased Poisson-gamma Lindley distribution with application, Eur. J. Stat., 2021, 1 (1), 132–147.
• [12] SU J.C., HUANG W.J., Characterisations based on conditional expectations, Stat. Pap., 2000, 41, 423–435.