Abstract
This chapter presents an algorithm for computing the PDF of order statistics drawn from discrete parent populations, along with an implementation of the algorithm in APPL. Several examples illustrate the utility of this algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. SIAM, Philadelphia
Burr IW (1955) Calculation of exact sampling distribution of ranges from a discrete population. Ann Math Stat 26:530–532 (correction, volume 38, 280)
Casella G, Berger R (2002) Statistical inference, 2nd edn. Duxbury, Pacific Grove, California
Ciardo G, Leemis LM, Nicol D (1995) On the minimum of independent geometrically distributed random variables. Stat Probab Lett 23:313–326
David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, New York
Evans DL, Leemis LM, Drew JH (2006) The distribution of order statistics for discrete random variables with applications to bootstrapping. INFORMS J Comput 18:19–30
Hogg RV, Craig AT (1995) Introduction to the mathematical statistics, 5th edn. Prentice-Hall, Upper Saddle River, New Jersey
Hogg RV, McKean JW, Craig AT (2005) Introduction to the mathematical statistics, 6th edn. Prentice-Hall, Upper Saddle River, New Jersey
Margolin BH, Winokur HS (1967) Exact moments of the order statistics of the geometric distribution and their relation to inverse sampling and reliability of redundant systems. J Am Stat Assoc 62:915–925
Rice JA (2007) Mathematical statistics and data analysis, 3rd edn. Thompson and Brooks/Cole, Belmont, California
Srivastava RC (1974) Two characterizations of the geometric distribution. J Am Stat Assoc 69:267–269
Young DH (1970) The order statistics of the negative binomial distribution. Biometrika 57:181–186
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Drew, J.H., Evans, D.L., Glen, A.G., Leemis, L.M. (2017). Order Statistics for Random Sampling from Discrete Populations. In: Computational Probability. International Series in Operations Research & Management Science, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-319-43323-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-43323-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43321-9
Online ISBN: 978-3-319-43323-3
eBook Packages: Business and ManagementBusiness and Management (R0)