References
- Eisenberg B, Stengle G, Strang G. The asymptotic probability of a tie for first place. Ann Appl Probab. 1993;3:731–745. doi: 10.1214/aoap/1177005360
- Brands JJAM, Steutel FW, Wilms RJG. On the number of maxima of a discrete sample. Statist Probab Lett. 1994;20:209–218. doi: 10.1016/0167-7152(94)90044-2
- Qi Y. A note on the number of maxima in a discrete sample. Statist Probab Lett. 1997;33:373–377. doi: 10.1016/S0167-7152(96)00150-2
- Bruss FT, Grübel R. On the multiplicity of the maximum in a discrete random sample. Ann Appl Probab. 2003;13:1252–1263. doi: 10.1214/aoap/1069786498
- Berred A, Stepanov A, Ties for the the second place. In: Ahsanullah M, Raqab M. editors. Recent developments in ordered random variables. New York: Nova Science Publisher; 2005. p. 171–185.
- Eisenberg B. The numbers of players tied for the record. Statist Probab Lett. 2009;79:283–288. doi: 10.1016/j.spl.2008.08.007
- Gouet R, López FJ, Sanz G. Limit laws for the cumulative number of ties for the maximum in a random sequence. J Statist Plann Inference. 2009;139:2988–3000. doi: 10.1016/j.jspi.2009.02.001
- Pakes A, Steutel FW. On the number of records near the maximum. Aust J Statist. 1997;39:179–193. doi: 10.1111/j.1467-842X.1997.tb00534.x
- Pakes A, Li Y. Limit laws for the number of near maxima via the Poisson approximation. Statist Probab Lett. 1998;40:395–401. doi: 10.1016/S0167-7152(98)00148-5
- Balakrishnan N, Stepanov A. A note on the number of observations near an order statistic. J Statist Plann Inference. 2005;134:1–14. doi: 10.1016/j.jspi.2004.01.018
- Dembińska A, Stepanov A, Wesołowski J. How many observations fall in a neighborhood of an order statistic? Comm Statist Theory Methods. 2007;36:851–867. doi: 10.1080/03610920601041523
- Dembińska A. Asymptotic properties of numbers of observations in random regions determined by central order statistics. J Statist Plann Inference. 2012;142:516–528. doi: 10.1016/j.jspi.2011.08.009
- Dembińska A, Iliopoulos G. On the asymptotics of numbers of observations in random regions determined by order statistics. J Multivariate Anal. 2012;103:151–160. doi: 10.1016/j.jmva.2011.06.016
- Li Y, Pakes A. On the number of near-maximum insurance claims. Insurance Math Econom. 2001;28:309–323. doi: 10.1016/S0167-6687(00)00080-9
- Hashorva E. On the number of near-maximum insurance claim under dependence. Insurance Math Econom. 2003;32:37–49. doi: 10.1016/S0167-6687(02)00192-0
- Hashorva E. Bivariate maximum insurance claim and related point processes. Statist Probab Lett. 2004;69:117–128. doi: 10.1016/j.spl.2004.06.008
- Müller S. Tail estimation based on numbers of near m-extremes. Methodol Comput Appl Probab. 2003;5:197–210. doi: 10.1023/A:1024509818767
- Hashorva E, Hüsler J. Estimation of tails and related quantities using the number of near-extremes. Comm Statist Theory Methods. 2004;34:337–349. doi: 10.1081/STA-200047414
- Iliopoulos G, Dembińska A, Balakrishnan N. Asymptotic properties of numbers of observations near sample quantiles. Statistics. 2012;46:85–97. doi: 10.1080/02331888.2010.498045
- Pakes A. Numbers of observations near order statistics. Aust N Z J Stat. 2009;51:375–395. doi: 10.1111/j.1467-842X.2009.00551.x
- Hashorva E, Macci C, Pacchiarotti B. Large deviations for proportions of observations which fall in random sets determined by order statistics. Methodol Comput Appl Probab. 2013;15:875–896. doi: 10.1007/s11009-012-9290-y
- Nagaraja HN, Bharah K, Zhang F. Spacings around an order statistic. Ann Inst Statist Math. 2015;67:515–540. doi: 10.1007/s10463-014-0466-9
- Dembińska A. Asymptotic normality of numbers of observations in random regions determined by order statistics. Statistics. 2014;48:508–523. doi: 10.1080/02331888.2012.748773
- Dembińska A. Limit theorems for proportions of observations falling into random regions determined by order statistics. Aust N Z J Stat. 2012;54(2):199–210. doi: 10.1111/j.1467-842X.2012.00667.x
- Dembińska A. Asymptotic behavior of central order statistics from stationary sequences. Stochastic Process Appl. 2014;124:348–372. doi: 10.1016/j.spa.2013.08.001
- Bradley RC. Introduction to strong mixing conditions. Vol. 1. Heber City (UT): Kendrick Press; 2007.
- Grimmet GR, Stirzaker DR. Probability and random processes. New York: Oxford University Press; 2004.
- Stein EM, Shakarchi R. Real analysis: measure theory, integration, and Hilbert spaces. Princeton: Princeton University Press; 2005.
- Hannan EJ. Multiple time series. New York: John Wiley and Sons; 1970.
- Feldman D, Tucker HG. Estimation of non-unique quantiles. Ann Math Statist. 1966;37:451–457. doi: 10.1214/aoms/1177699527