Abstract
The exact probability density function of linear combinations of k=k(n) order statistics selected from the whole order statistics (L-statistic) based on a random sample of size n from the uniform distribution on [0, 1] was derived by Matsunawa (1985, Ann. Inst. Statist. Math., 37, 1–16). As the main expression for the density function given by Matsunawa is not complete for the general situation, we first provide the corrections for this formula. Second, we propose a simple scheme involving symbolic computing for evaluating the corrected version of the density function. The cumulative distribution function and the r-th mean of his L-statistic are also derived.
Similar content being viewed by others
References
D'Agostino, R. B. and Stephens, M. A. (1986). Goodness-of-Fit Techniques, Marcel Dekker, New York.
Kochar, S. C. (1984). Testing goodness-of-fit in terms of the failure rate function, IAPQR Trans., 9, 1–6.
Kochar, S. C. and Ramallingam, T. (1989). Testing for superadditivity of the mean value function of a non-homogeneous Poisson process, Comm. Statist. A—Theory Methods, 18, 1549–1562.
Matsunawa, T. (1985). The exact and approximate distributions of linear combinations of selected order statistics from a uniform distribution, Ann. Inst. Statist. Math., 37, 1–16.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.
Seward, L. R. (1985). REDUCE User's Guide for IBM 360 and Derivative Computers, Version 3.2, The Rand Corporation, Santa Monica, California.
Author information
Authors and Affiliations
About this article
Cite this article
Ramallingam, T. Symbolic computing the exact distributions of L-statistics from a uniform distribution. Ann Inst Stat Math 41, 677–681 (1989). https://doi.org/10.1007/BF00057734
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00057734