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2017 | OriginalPaper | Chapter

9. Order Statistics for Random Sampling from Discrete Populations

Authors : John H. Drew, Diane L. Evans, Andrew G. Glen, Lawrence M. Leemis

Published in: Computational Probability

Publisher: Springer International Publishing

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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.

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Literature
5.
go back to reference Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. SIAM, Philadelphia Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. SIAM, Philadelphia
14.
go back to reference Burr IW (1955) Calculation of exact sampling distribution of ranges from a discrete population. Ann Math Stat 26:530–532 (correction, volume 38, 280) Burr IW (1955) Calculation of exact sampling distribution of ranges from a discrete population. Ann Math Stat 26:530–532 (correction, volume 38, 280)
16.
go back to reference Casella G, Berger R (2002) Statistical inference, 2nd edn. Duxbury, Pacific Grove, California Casella G, Berger R (2002) Statistical inference, 2nd edn. Duxbury, Pacific Grove, California
17.
go back to reference Ciardo G, Leemis LM, Nicol D (1995) On the minimum of independent geometrically distributed random variables. Stat Probab Lett 23:313–326CrossRef Ciardo G, Leemis LM, Nicol D (1995) On the minimum of independent geometrically distributed random variables. Stat Probab Lett 23:313–326CrossRef
20.
30.
go back to reference Evans DL, Leemis LM, Drew JH (2006) The distribution of order statistics for discrete random variables with applications to bootstrapping. INFORMS J Comput 18:19–30CrossRef Evans DL, Leemis LM, Drew JH (2006) The distribution of order statistics for discrete random variables with applications to bootstrapping. INFORMS J Comput 18:19–30CrossRef
50.
go back to reference Hogg RV, Craig AT (1995) Introduction to the mathematical statistics, 5th edn. Prentice-Hall, Upper Saddle River, New Jersey Hogg RV, Craig AT (1995) Introduction to the mathematical statistics, 5th edn. Prentice-Hall, Upper Saddle River, New Jersey
52.
go back to reference Hogg RV, McKean JW, Craig AT (2005) Introduction to the mathematical statistics, 6th 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
81.
go back to reference 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 62:915–925CrossRef 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 62:915–925CrossRef
103.
go back to reference Rice JA (2007) Mathematical statistics and data analysis, 3rd edn. Thompson and Brooks/Cole, Belmont, California Rice JA (2007) Mathematical statistics and data analysis, 3rd edn. Thompson and Brooks/Cole, Belmont, California
110.
go back to reference Srivastava RC (1974) Two characterizations of the geometric distribution. J Am Stat Assoc 69:267–269CrossRef Srivastava RC (1974) Two characterizations of the geometric distribution. J Am Stat Assoc 69:267–269CrossRef
123.
go back to reference Young DH (1970) The order statistics of the negative binomial distribution. Biometrika 57:181–186CrossRef Young DH (1970) The order statistics of the negative binomial distribution. Biometrika 57:181–186CrossRef
Metadata
Title
Order Statistics for Random Sampling from Discrete Populations
Authors
John H. Drew
Diane L. Evans
Andrew G. Glen
Lawrence M. Leemis
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-43323-3_9

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