Evaluating improvements of records

• Autorzy: Tomasz Rychlik
• Języki publikacji: EN

Abstrakty

EN

We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

Słowa kluczowe

EN

monotone failure rate; monotone failure probability; record value; projection; sharp bound; variance; central absolute moment; independent identically distributed variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 3
• Strony: 315-324

Daty

wydano

1997

otrzymano

1996-05-16

Twórcy

autor

Tomasz Rychlik

• Institute of Mathematics, Polish Academy of Sciences, ul. Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] M. Ahsanullah, Linear predictions of record values for two parameter exponential distribution, Ann. Inst. Statist. Math. 32 (1980), 363-368.
• [2] A. V. Balakrishnan, Applied Functional Analysis, 2nd ed., Springer, New York, 1981.
• [3] I. R. Dunsmore, The future occurrence of records, Ann. Inst. Statist. Math. 35 (1983), Part A, 267-277.
• [4] L. Gajek and T. Rychlik, Projection method for moment bounds on order statistics from restricted families. I. Dependent case, J. Multivariate Anal. 57 (1996), 156-174.
• [5] S. Moriguti, A modification of Schwarz's inequality with applications to distributions, Ann. Math. Statist. 24 (1953), 107-113.
• [6] H. N. Nagaraja, On the expected values of record values, Austral. J. Statist. 20 (1978), 176-182.
• [7] V. B. Nevzorov, Records, Teor. Veroyatnost. i Primenen. 32 (1987), 219-251 (in Russian).
• [8] W. R. van Zwet, Convex Transformations of Random Variables, Mathematisch Centrum, Amsterdam, 1964.