74ccdf55-7ec1-45a5-bf07-a0d86ab7ea4c20220608093248177wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511520221520222110.37394/23206.2022.21https://wseas.com/journals/mathematics/2022.phpM. I.KhanDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, SAUDI ARABIAThe paper highlights the moments characteristics of the doubly truncated power hazard rate distribution via generalized order statistics. The particular cases and several deductions are explained. The characterization result has also deliberated. Additionally, some numerical computations through R software are listed.68202268202233834239https://wseas.com/journals/mathematics/2022/a785106-018(2022).pdf10.37394/23206.2022.21.39https://wseas.com/journals/mathematics/2022/a785106-018(2022).pdf10.1016/j.amc.2004.09.064Mugdadi, A. R., The least squares type estimation of the parameters in the power hazard function, Applied Mathematics Computation, Vol. 169, 2005, pp. 737–748. Ismail, K., Estimation of 𝑃(𝑌 < 𝑋) for distribution having power hazard function, Pakistan Journal of Statistics, Vol. 30, 2014, pp. 57–70. 10.4064/am-20-4-531-542Mailhot, L., Some properties of truncated distributions connected with log-concavity of distribution functions, Applicationes Mathematicae, Vol. 20, No. 4, 1988, pp.531– Salah, H. A., Properties of doubly truncated Fréchet distribution, American Journal of Applied Mathematics and Statistics, Vol. 4, No.1, 2016, pp. 9-15. Kamps, U., A Concept of Generalized Order Statistics. B.G. Teubner Stuttgart, Germany, 1995. Ahsanullah, M. and Nevzorov, V. B., Ordered Random Variables, Nova Science Publishers, USA, 2001. 10.2991/978-94-6239-225-0Shahbaz, M. Q., Ahsanullah, M., Hanif Shahbaz, S. and Al-Zahrani, B., Ordered Random Variables: Theory and Applications, Atlantis Studies in Probability and Statistics, Springer, 2016. 10.1016/s0378-3758(02)00385-3Ahmad, A. A. and Fawzy, A. M., Recurrence relations for single moments of generalized order statistics from doubly truncated distributions, Journal of Statistical and Planning Inference, Vol. 117, 2013, pp. 241-249. 10.1016/j.joems.2013.12.014Ahmad, A. A., Recurrence relations for single and product moments of generalized order statistics from doubly truncated Burr type XII distribution, Journal of Egyptian Mathematical Society, Vol.15, 2007, pp. 117-128. 10.18642/jsata_7100121978Khan, R. U., Anwar, Z. and Athar, H., Recurrence relations for single and product moments of generalized order statistics from doubly truncated Weibull distribution, Aligarh Journal of Statistics, Vol. 27, 2007, pp. 69–79. 10.12785/msl/020102Kumar, D. and Khan, M. I., Relations for generalized order statistics from doubly truncated generalized exponential distribution and its characterization, Mathematical Science Letter, Vol. 2, No. 1, 2013, pp. 9-18. Khan, R. U. and Zia, B., Generalized order statistics of doubly truncated linear exponential distribution and a characterization, Journal of Applied Probability and Statistics, Vol. 9, No.1, 2014, pp. 53-65 10.37394/23206.2021.20.64Jamal, F. and Chesneau, C., The Moment Properties of Order, Reversed Order and Upper Record Statistics for the Power Ailamujia Distribution, WSEAS Transactions on Mathematics, Vol. 20, 2021, pp. 607-614. Khan, M.I., Moments of generalized order statistics from doubly truncated power-linear hazard rate distribution, Statistics Optimization, and Information Computing, 2022, (Accepted). Khan, M. I., The distribution having power hazard function based on ordered random variable, Journal of Statistics Applications & Probability Letter, Vol. 4, No.1, 2017, pp. 33-36. 10.18576/jsap/080204Khan, M. I. and Khan, M. A. R, Generalized record values from distributions having power hazard function and characterization, Journal of Statistics Applications & Probability, Vol. 8, No. 2, 2019, pp.103-111. Hwang, J. S. and Lin, G. D., Extensions of MuntzSzasz theorems and application, Analysis, Vol. 4, No. 1-2, 1984, pp.143–160.