8e87a574-3212-4e0e-b18b-debc1244c5be20211123061513301wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40513220213220212010.37394/23206.2021.20https://wseas.org/wseas/cms.action?id=23278The Moment Properties of Order, Reversed Order and Upper Record Statistics for the Power Ailamujia DistributionFarrukhJamalDepartment of Statistics, The Islamia University of Bahawalpur, Punjab 63100, PAKISTANChristopheChesneauDepartment of Mathematics, Université de Caen, LMNO, Campus II, Science 3, Caen 14032, FRANCEThe power Ailamujia distribution has been successfully developed in statistics, both theoretically and practically, performing well in the fitting of various types of data. This paper investigates the moment properties of the associated order, reversed order and upper record statistics, which are indeed unexplored aspects of this distribution. In particular, the exact expressions for the single moments of the order and reversed order statistics are provided. Some recurrence relationships for both single and product moments for the order and upper record statistics are proved. For additional goals, certain joint distributions are also given.111820211118202160761464https://wseas.com/journals/mathematics/2021/b305106-1490.pdf10.37394/23206.2021.20.64https://wseas.com/journals/mathematics/2021/b305106-1490.pdfLv, H.Q., Gao, L.H. and Chen, C.L. (2002). Ailamujia distribution and its application in supportability data analysis, Journal of Academy of Armored Force Engineering, 16, 48-52. Ul Ain, S.Q., Aijaz, A. and Tripathi, R. (2020). A new two parameter Ailamujia distribution with applications in bio-medicine, Journal of Xi’an University of Architecture & Technology, 12, 11, 592-604. Jamal, F., Chesneau, C., Aidi, K. and Ali, A. (2021). Theory and application of the power Ailamujia distribution, Journal of Mathematical Modeling, 9, 3, 391-413. 10.1002/nav.3800300307Khan, A.H., Yaqub, M. and Parvez, S. (1983a). Recurrence relations between moments of order statistics, Naval Research Logistics Quarterly, 30, 419-441. 10.1016/0378-3758(83)90036-8Khan, A.H., Parvez, S. and Yaqub, M. (1983b). Recurrence relations between product moments of order statistics, Journal of Statistical Planning and Inference, 8, 175-183. 10.1080/0233188032000158781Raqab, M.Z. (2004). Generalized exponential distribution: moments of order statistics, Statistics 38, 1, 29-41. 10.1007/s00362-006-0377-9Thomas, P.Y. and Samuel, P. (2008). Recurrence relations for the moments of order statistics from a beta distribution, Statistical Papers, 49, 139- 146. 10.2991/jsta.d.210602.001Saran, J., Verma, K. and Pushkarna, N. (2018). Relationships for moments of generalized order statistics from Erlang-truncated exponential distribution and related inference, ProbStat Forum, 11, 91-103. 10.1080/00949655.2016.1163361Sultan, K.S. and AL-Thubyani, W.S. (2016). Higher order moments of order statistics from the Lindley distribution and associated inference, Journal of Statistical Computation and Simulation, 86, 17, 3432-3445. 10.1111/j.2517-6161.1952.tb00115.xChandler, K.N. (1952). The distribution and frequency of record values, Journal of the Royal Statistical Society: Series B, 14, 220-228. Saran, J. and Pushkarna, N. (2000). Relationships for moments of record values from linearexponential distribution, Journal of Applied Statistical Science, 10, 69-76. 10.3923/ajms.2008.159.164Saran, J. and Singh, S.K. (2008). Recurrence relations for single and product moments of k-th record values from linear-exponential distribution and a characterization, Asian Journal of Mathematics and Statistics, 1, 3, 159-164. 10.12988/imf.2007.07184Sultan, K.S. (2007). Record values from the modified Weibull distribution, International Mathematical Forum, 2, 41, 2045-2054. 10.2991/978-94-6239-225-0_6Shahbaz, M.Q., Ahsanullah, M., Hanif Shahbaz, S and Al-Zahrani, B. (2016). Ordered Random Variables: Theory and Applications, Atlantis Press and Springer, France. 10.1023/a:1016178914240Bieniek, M. and Szynal, D. (2002). Recurrence relations for distribution functions and moments of kth record values, Journal of Mathematical Sciences, 111, 3, 3511-3519.