Abstract
In this paper, we first derive exact explicit expressions for the triple and quadruple moments of order statistics from the power function distribution. Also, we present recurrence relations for single, double, triple and quadruple moments of order statistics from the power function distribution. These relations will enable one to find all moments (of order up to four) of order statistics for all sample sizes in a simple recursive manner. We then use these results to determine the mean, variance, and coefficients of skewness and kurtosis of certain linear functions of order statistics. We then derive approximate confidence intervals for the parameters of the power function distribution using the Edgeworth approximation. Finally, we extend the recurrence relations to the case of the doubly truncated power function distribution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992). A First Course in Order Statistics, New York: John Wiley & Sons.
Balakrishnan, N. and Cohen, A. C. (1991). Order Statistics and Inference: Estimation Methods, San Diego: Academic Press.
Balakrishnan, N. and Gupta, S. S. (1996). Higher order moments of order statistics from exponential and right-truncated exponential distributions and applications to life-testing problems, In Handbook of Statistics-16: Order Statistics and Their Applications (Eds., C. R. Rao and N. Balakrishnan), Amsterdam: North-Holland (to appear).
Balakrishnan, N. and Joshi, P. C. (1981). Moments of order statistics from doubly truncated power function distribution, Aligarh Journal of Statistics, 1, 98–105.
. Balakrishnan, N., Childs, A., Govindarajulu, Z. and Chandramouleeswaran, M. P. (1996). Inference on parameters of the Laplace distribution based on Type-II censored samples using Edgeworth approximation, submitted for publication.
Barton, D. E. and Dennis, K. E. R. (1952). The conditions under which Gram-Charlier and Edgeworth curves are positive definite and unimodal, Biometrika, 39, 425–427.
Childs, A. and Balakrishnan, N. (1996). Generalized recurrence relations for moments of order statistics from non-identical Pareto and truncated Pareto random variables with applications to robustness, In Handbook of Statistics-16: Order Statistics and Their Applications (Eds., C. R. Rao and N. Balakrishnan), Amsterdam: North-Holland (to appear).
. Childs, A., Sultan, K. S. and Balakrishnan, N. (1996). Higher order momentss of order statistics from the Pareto distribution and Edgeworth approximate inference, submitted for publication.
David, H. A. (1981). Order Statistics, Second edition, New York: John Wiley & Sons.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1, Second edition, New York: John Wiley & Sons.
Malik, H. J. (1967). Exact moments of order statistics from a power function distribution, Skandinavisk Aktuarietidskrift, 64–69.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sultan, K.S., Childs, A., Balakrishnan, N. (2000). Higher Order Moments of Order Statistics From the Power Function Distribution and Edgeworth Approximate Inference . In: Balakrishnan, N., Melas, V.B., Ermakov, S. (eds) Advances in Stochastic Simulation Methods. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1318-5_15
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1318-5_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7091-1
Online ISBN: 978-1-4612-1318-5
eBook Packages: Springer Book Archive