The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping

References

• Andrews D. W. K., Buchinsky M. On the number of bootstrap repetitions for BCa confidence intervals. Econometric Theory (2002) 18:962–984Crossref, Google Scholar
• Andrews D. W. K., Buchinsky M. A three-step method for choosing the number of bootstrap repetitions. Econometrica (2000) 68:23–51Crossref, Google Scholar
• Arnold B. C., Balakrishnan N., Nagaraja H. N.A First Course in Order Statistics (1992) (Wiley, New York) Google Scholar
• Balakrishnan N. Recurrence relations for order statistics from n independent and non-identically distributed random variables. Ann. Inst. Statist. Math. (1988) 40:273–277Crossref, Google Scholar
• Balakrishnan N., Bendre S. M., Malik H. J. General relations and identities for order statistics from non-independent non-identical variables. Ann. Inst. Statist. Math. (1992) 44:177–183Crossref, Google Scholar
• Balakrishnan N., Rao C. R.Order Statistics: Applications (1998) (Elsevier, Amsterdam, The Netherlands) Google Scholar
• Bapat R. B., Beg M. I. Identities and recurrence relations for order statistics corresponding to non-identically distributed variables. Comm. Statist. Theory Methods (1989) 18:1993–2004Crossref, Google Scholar
• Boncelet C. G. Algorithms to compute order statistic distributions. SIAM J. Statist. Comput. (1987) 8:868–876Crossref, Google Scholar
• Burr I. W. Calculation of exact sampling distribution of ranges from a discrete population. Ann. Math. Statist. (1955) 26:530–532Correction 38 280Crossref, Google Scholar
• Cao G., West M. Computing distributions of order statistics. Comm. Statist. Theory Methods (1997) 26:755–764Crossref, Google Scholar
• Casella G., Berger R.Statistical Inference (2002) 2nd ed.(Duxbury Press, Pacific Grove, CA) Google Scholar
• Ciardo G., Leemis L., Nicol D. On the minimum of independent geometrically distributed random variables. Statist. Probab. Lett. (1995) 23:313–326Crossref, Google Scholar
• David H. A., Nagaraja H. N.Order Statistics (2003) 3rd ed.(Wiley, Hoboken, NJ) Crossref, Google Scholar
• Efron B., Tibshirani R.An Introduction to the Bootstrap (1993) (Chapman & Hall, New York) Crossref, Google Scholar
• Glen A., Leemis L., Evans D. APPL: A probability programming language. Amer. Statistician (2001) 55:156–166Crossref, Google Scholar
• Hand D. J., Daly F., Lunn A. D., McConway K. J., Ostrowski E.A Handbook of Small Data Sets (1994) (Chapman & Hall, London, UK) Crossref, Google Scholar
• Hogg R. V., Craig A. T.Mathematical Statistics (1995) 5th ed.(Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Hutson A. D., Ernst M. D. The exact bootstrap mean and variance of an L-estimator. J. Roy. Statist. Soc. B (2000) 62:89–94Crossref, Google Scholar
• Margolin B. H., Winokur Jr. H. S. Exact moments of the order statistics of the geometric distribution and their relation to inverse sampling and reliability of redundant systems. J. Amer. Statist. Assoc. (1967) 62:915–925Crossref, Google Scholar
• Nagaraja H. N., Sen P. K., Morrison D. F.Statistical Theory and Applications: Papers in Honor of Herbert A. David (1996) (Springer, New York) Crossref, Google Scholar
• Rice J. A.Mathematical Statistics and Data Analysis (1995) 2nd ed.(Wadsworth, Belmont, CA) Google Scholar
• Srivastava R. C. Two characterizations of the geometric distribution. J. Amer. Statist. Assoc. (1974) 69:267–269Crossref, Google Scholar
• Trosset M. (2001) . Personal communicationGoogle Scholar
• Young D. H. The order statistics of the negative binomial distribution. Biometrika (1970) 57:181–186Crossref, Google Scholar
• Young G. A. Bootstrap: More than a stab in the dark? Statist. Sci. (1994) 9:382–415Crossref, Google Scholar