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Records from a power model of independent observations

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ishay Weissman
Ishay Weissman*
Affiliation:
Technion — Israel Institute of Technology
*
∗Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
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Abstract

Records from are analyzed, where {Yj} is an independent sequence of random variables. Each Yj has a continuous distribution function Fj = Fλj for some distribution F and some λ j > 0. We study records, record times and related quantities for this sequence. Depending on the sequence of powers , a wide spectrum of behaviour is exhibited.

Keywords

EXTREMAL PROCESSESREGULARLY VARYING SEQUENCESUNIFORMASYMPTOTIC NEGLIGIBILITY

MSC classification

Primary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 982 - 990
Copyright
Copyright © Applied Probability Trust 1995 

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References

Ballerini, R. and Resnick, S. (1985) Records from improving populations. J. Appl. Prob. 22, 487–502.Google Scholar
Ballerini, R. and Resnick, S. (1987a) Records in the presence of a linear trend. Adv. Appl. Prob 19, 801–828.Google Scholar
Ballerini, R. and Resnick, S. (1987b) Embedding sequences of successive maxima in extremal processes with applications. J. Appl. Prob. 24, 827–837.Google Scholar
Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Deheuvels, P. and Nevzorov, V. B. (1994) Records in the Fa-scheme. I. Martingale properties. Notes Sci. Semin. POMI 207, 19–36.Google Scholar
Galambos, J. (1987) The Asymptotic Theory of Extreme Order Statistics, 2nd end. Robert E. Krieger Pub. Co., Malabar, Florida.Google Scholar
Glick, N. (1978) Breaking records and breaking boards. Amer. Math. Monthly 85, 2–26.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series and Products. Academic Press, New York.Google Scholar
De Haan, L. and Verkade, E. (1987) On extreme value theory in the presence of a trend. J. Appl. Prob. 24, 62–76.Google Scholar
De Haan, L. and Weissman, I. (1988) The index of the outstanding observation among n independent ones. J. Stoch. Proc. Appl. 27, 317–329.Google Scholar
Loeve, M. (1963) Probability Theory, 3rd edn. Van Nostrand, Princeton, NJ.Google Scholar
Nevzorov, V. B. (1988) Records. Theor. Prob. Appl. 32, 201–228.CrossRefGoogle Scholar
Resnick, S. (1987) Extreme Values, Regular Variation and Point Processes. Springer-Verlag, New York.Google Scholar
Resnick, S. and Roy, R. (1990) Multivariate extremal processes, leader processes and dynamic choice models. Adv. Appl. Prob. 22, 309–331.Google Scholar
Shorrock, R. W. (1972) On record values and records times. J. Appl. Prob. 9, 316–326.Google Scholar
Smith, R. L. (1988) Forecasting records by maximum likelihood. J. Amer. Statist. Assoc. 83, 331–338.CrossRefGoogle Scholar
Smith, R. L. and Miller, J. E. (1984) Predicting records. Technical Report, Department of Mathematics, Imperial College, London.Google Scholar
Smith, R. L. and Miller, J. E. (1986) A non-Gaussian state space model and applications to the prediction of records. J. R. Statist. Soc. B48, 79–88.Google Scholar
Weissman, I. (1976) On weak convergence of extremal processes. Ann. Prob. 4, 470–473.Google Scholar
Yang, M. C. K. (1975) On the distribution of the inter-record times in an increasing population. J. Appl. Prob. 12, 148–154.CrossRefGoogle Scholar