Journal of Statistical Research ISSN 0256 - 422 X 2007, Vol. 41, No. 1, pp. 37–50 Bangladesh MOMENTS OF ORDER STATISTICS FROM DOUBLY TRUNCATED BURR XII DISTRIBUTION: A COMPLEMENTARY NOTE WITH APPLICATIONS Shola Adeyemi 1 Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria. Email: sholadeyemi2003@yahoo.com Atinuke O. Adebanji Department of Statistics, University of Agriculture, Abeokuta 11001, Nigeria. Email: tinuadebanji@yahoo.com summary By using some distributional properties, we obtain some results on recurrence re- lations for single and product moments of order statistics from doubly truncated Burr XII distribution. These results complement earlier results of Begum and Parvin [2002], as well as, generalize results obtained by Balakrishnan and Gupta [1998], Balakrishnan et al. [1994], and Saran and Pushkarna [1999]. Simulation results are consistent with those obtained by Begum and Parvin [2002] and are given for single and product moments in Tables 1 and 2. Applications to least squares estimation of the Best Linear Unbiased Estimates of location-scale pa- rameters involving singly and doubly censored life-testing data are considered. The estimation results compare favorably with those by Balakrishnan and Gupta [1998] in estimating the scale parameter of the censored data using the exponen- tial distribution. Keywords and phrases: order statistics; Burr XII distribution; single and product moments; truncation. 1 Introduction The Burr distribution is very important in modelling of ﬁnance and insurance data. Ex- perience has shown that the Pareto formula is often an appropriate model for claim size distribution, particularly where exceptionally large claims may occur. However, there is sometimes a need to ﬁnd heavy tailed distributions which oﬀer greater ﬂexibility than the Pareto law. Such ﬂexibility is provided by the Burr distribution with distribution function given by c  Institute of Statistical Research and Training (ISRT), University of Dhaka, Dhaka 1000, Bangladesh. 1 Current Address: Health and Social Care Modelling Group, University of Westminster, London, United Kingdom