Ignatov's theorem
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In statistics, Ignatov's theorem (named after Prof. Tzvetan Ignatov, a Bulgarian mathematician, currently a professor at Sofia University) states that for an infinite sequence of independent and identically distributed i.i.d. random variables, the k-record process, consisting of those terms that are the k-th largest at their appearance, is i.i.d.
References
1. Adler, I., Ross, S.M., 1997. Distribution of the time of the :rst k-record. Probab. Eng. Inform. Sci. 11, 273–278. 2. Engelen, R., Thommassen, P., Vervaat, W., 1988. Ignatov’s theorem – a new andshort proof. J. Appl. Probab. 25 (a), 229–236. 3. Ignatov, Z. 1977., Ein von der Variationsreihe erzeugter Poissonscher Punktprozess. Annuaire Univ. Sofia Fac. Math. Mech. 71 79-94 (published 1986). 4. Ignatov, Z., 1978. Point processes generated by order statistics and their applications. In: P. Bartfai and J. Tomko, eds., Point Processes and Queueing Problems, Keszthely (Hungary). Coll. Mat. Soc. 5. Janos Bolyai 24, North-Holland, Amsterdam, 109–116. Samuels, S., 1992. All at once proof of Ignatov’s theorem. Contemp. Math. 125, 231–237. 5. Ross, S., 2003. Introduction to Probability Models, 8th edition, San Diego, CA: Academic Press.