ON THE MEAN AND VARIANCE OF A FUNCTION OF ORDER STATISTICS

Order statistics deals with the properties and applications of random variables and their functions. In this study the distribution of order statistics for samples is derived andTaylor?s expansion technique is applied for the calculation of moments ofthe functions. The transformation of random variable X, i.e. h(X) has been computed in several ways as well and it is found that the variance of ln(X(m+1)) is negligible as compared to the variance of X(m+1). In this paper the probability distribution of ln(X(m+1)) is completely evaluated for large samples.