© 2009 Pakistan Journal of Statistics 327 Pak. J. Statist. 2010 Vol. 26(2), 327-337 MOMENTS OF ORDER STATISTICS FROM A GENERAL CLASS OF DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS Jagdish Saran and N. Pushkarna Department of Statistics, University of Delhi, Delhi 110 007, India Email: jagdish_saran52@yahoo.co.in ABSTRACT In this paper we derive some general recurrence relations satisfied by the single and product moments of order statistics from a general class of doubly truncated distributions, which unify the earlier results in this direction due to several authors. KEYWORDS AND PHRASES Recurrence relations, single moments, product moments, truncated and non-truncated Lomax, Weibull, Weibull-gamma, Weibull-exponential, log logistic, exponential, generalized exponential, Rayleigh, generalized Rayleigh, generalized Pareto, linear- exponential and Burr distributions. 1. INTRODUCTION Order statistics and their moments have great importance in many statistical problems. Linear functions of order statistics are found to be extremely useful in the estimation of parameters and also in testing of hypotheses problems. Knowledge of the moments of order statistics, in particular their means, variances and covariances, allows us to evaluate the expected value and variance of a linear function of order statistics, and hence permits us to obtain estimators and their efficiencies. With the primary intention of reducing the amount of direct computation of these moments, many authors have investigated and derived several recurrence relations and identities satisfied by these moments of order statistics. For more details, see Malik, Balakrishnan and Ahmed (1988), Balakrishnan, Malik and Ahmed (1988), Balakrishnan and Sultan (1998), Khan et al. (1983a,b), Ahmad (2001) and Saran and Pushkarna (1999a,b,c; 2000a,b). In some of these references, a particular distribution is considered and the recurrence relations for moments of order statistics are obtained by using the corresponding characterizing differential equation. Let 1: 2: : n n nn X X X   be the order statistics obtained from a population having an absolutely continuous cumulative distribution function (cdf) () Gx and a probability density function (pdf) () gx . Then the pdf of : rn X , 1 r n   , is given by     1 : { () 1 () ( ), , r n r rn C Gx Gx gx x      (1.1) and the joint pdf of : rn X and : (1 ) sn X r s n    is given by