Records: Mathematical Theory

Nevzorov, V. B.

doi:10.1090/mmono/194

Cited by 280 publications

(263 citation statements)

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“…The following result is classical in the asymptotic theory of order statistics (for proofs, discussions and generalizations, see [2,3,[5][6][7]). …”

Section: Some Facts From the Asymptotic Theory Of Order Statisticsmentioning

confidence: 99%

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Stopping rules in k-adaptive global random search algorithms

Zhigljavsky

Hamilton

2010

J Glob Optim

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“…The following result is classical in the asymptotic theory of order statistics (for proofs, discussions and generalizations, see [2,3,[5][6][7]). …”

Section: Some Facts From the Asymptotic Theory Of Order Statisticsmentioning

confidence: 99%

“…w = W k,n is the waiting time until the next update. Using the standard arguments used in the theory of k-th records (see, for example, [6], Lecture 19) we derive the distribution of W k,n .…”

Section: Waiting Time Until the Next Updatementioning

confidence: 99%

Stopping rules in k-adaptive global random search algorithms

Zhigljavsky

Hamilton

2010

J Glob Optim

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“…For an elaborate treatment on records and their applications, one may refer to the books by [6], [4] and [17]. For a detailed discussion on the Weibull records and associated inferences, one may refer to [22].…”

Section: Introductionmentioning

confidence: 99%

One-sequence and two-sequence prediction for future Weibull records

Bdair¹,

Raqab²

2016

JSTA

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Based on record data, prediction of the future records from the two-parameter Weibull distribution is studied. First we consider the sampling based procedure to compute the Bayes estimates and also to construct symmetric credible intervals. Secondly, we consider one-sequence and two-sequence Bayes prediction of the future records based on some observed records. The Monte Carlo algorithms are used to compute simulation consistent predictors and prediction intervals for future unobserved records. A numerical simulation study is conducted to compare the different methods and a real data set involving the annual rainfall recorded at Los Angeles Civic Center during 132 years is analyzed to illustrate the procedures developed here.

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“…Then, some of the relevant questions of interest are the probability for the occurrence of record at any given time, mean number of records in a certain time window and record age, i.e, how long a record is expected to survive. The result for most of these questions is known for uncorrelated random variables [13]. However, it is known that most of the physically observed time series, e.g, temperature, stock market volatility, earthquake magnitudes, are strongly correlated [14].…”

Section: Introductionmentioning

confidence: 99%

Record statistics of financial time series and geometric random walks

Sabir¹,

Santhanam²

2014

Phys. Rev. E

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The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5 ≤ α ≤ 1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that from the empirical stock data.

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Records: Mathematical Theory

Cited by 280 publications

References 0 publications

Stopping rules in k-adaptive global random search algorithms

Stopping rules in k-adaptive global random search algorithms

One-sequence and two-sequence prediction for future Weibull records

Record statistics of financial time series and geometric random walks

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