Bounds for the moments of extreme order statistics for large samples

Abstract

The object of this paper is to obtain some bounds and approximations to the moments of extreme order statistics in large, samples. These are of same form as those of SUGIURA [11]. The proposed method is applicable whenever a few moments of extreme order statistics for large sample sizes are available. Fourier coefficients useful for approximating the first two moments of normal order statistics are tabulated. Numerical calculations for normal distribution show that this method gives a considerable improvement over the method of SUGIURA.

Keywords:

• Approximations and bounds
• extremes
• Fourier coefficients. Legendre polynomials
• moments
• Normal distribution
• order statistics
• probability integral transformation