References
- Dziubdziela W, Kopociński B. Limiting properties of the kth record values. Zastos Mat. 1976;15:187–190.
- Nevzorov VB. Records: mathematical theory. Providence, RI: American Mathematical Society; 2000. (Translations of Mathematical Monographs, Vol. 194)
- Arnold BC, Balakrishnan N, Nagaraja HN. Records. New York: Wiley; 1998.
- Dembińska A, López-Blázquez F. kth records from discrete distributions. Statist Probab Lett. 2005;71:203–214. doi: 10.1016/j.spl.2004.11.001
- Klimczak M, Rychlik T. Maximum variance of kth records. Statist Probab Lett. 2004;69:421–430. doi: 10.1016/j.spl.2004.06.038
- Papadatos N. Maximum variance of order statistics. Ann Inst Statist Math. 1995;47:185–193. doi: 10.1007/BF00773423
- Jasiński K. On maximum variance of kth records. Commun Statist – Theory Methods. 2016;45:2392–2401. doi: 10.1080/03610926.2013.879895
- Nagaraja HN. On the expected values of record values. Austral J Statist. 1978;20:176–182. doi: 10.1111/j.1467-842X.1978.tb01303.x
- Grudzień Z, Szynal D, On the expected values of kth record values and associated characterizations of distributions. In: Konecny F, Mogyoródy J, Wertz W, editors. Probability and statistical decision theory, Vol. A. Dordrecht: Reidel; 1985. p. 119–127.
- Moriguti S. A modification of Schwarz's inequality with applications to distributions. Ann Math Statist. 1953;24:107–113. doi: 10.1214/aoms/1177729088
- Raqab MZ. Bounds based on the greatest convex minorants for moments of record values. Statist Probab Lett. 1997;36:35–41. doi: 10.1016/S0167-7152(97)00046-1
- Raqab MZ. On the moments of record values. Commun Statist – Theory Methods. 2000;29:1631–1647. doi: 10.1080/03610920008832569
- Raqab MZ, Rychlik T. Sharp bounds for the mean of kth record value. Commun Statist – Theory Methods. 2002;31:1927–1937. doi: 10.1081/STA-120015011
- Danielak K. Distribution-free bounds for expectations of increments of records. J Statist Plann Inference. 2005;133:239–247. doi: 10.1016/j.jspi.2004.01.010
- Rychlik T. Evaluating improvements of records. Appl Math (Warsaw). 1997;24:315–324.
- Danielak K, Raqab MZ. Sharp upper bounds for expectations of kth record increments. Austral NZ J Statist. 2004;46:665–673. doi: 10.1111/j.1467-842X.2004.00361.x
- Danielak K, Raqab MZ. Sharp upper bounds on expectations of kth record spacings from restricted families. Statist Probab Lett. 2004;69:175–187. doi: 10.1016/j.spl.2004.06.027
- Raqab MZ, Rychlik T. Sharp bounds on the expectations of second record values from symmetric populations. Statistics. 2004;38:49–57. doi: 10.1080/0233188032000158808
- Raqab MZ. Sharp bounds on expectations of second record increments from decreasing density families. J Statist Plann. Inference. 2007;137:1291–1301. doi: 10.1016/j.jspi.2006.02.008
- Kozyra PM, Rychlik T. Sharp bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units. Probab. Math. Statist., forthcoming.
- Hoeffding W. Maßtabinvariante Korrelations-Theorie. Schrift Math Inst Univ Berlin. 1940;5:181–233.
- Lehmann EL. Some concepts of dependence. Ann Math Statist. 1966;37:1137–1153. doi: 10.1214/aoms/1177699260
- Bronshtein IN, Semendyayev KA, Musiol G, Mühlig H. Handbook of mathematics. 6th ed. Heidelberg: Springer; 2015.
- Komornik V. Another short proof of Descartes's rule of signs. Amer Math Monthly. 2006;113:829–830. doi: 10.2307/27642066