Return interval distribution of extreme events and long-term memory

Santhanam, M. S.; Kantz, Holger

doi:10.1103/physreve.78.051113

Cited by 108 publications

(77 citation statements)

References 42 publications

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“…This type of behavior is different from e.g. fully developed hydrodynamic turbulence, which is better described by lognormal superstatistics [2], or wind velocity fluctuations, described by inverse χ 2 superstatistics [19,23]. In future work one might aim to develop a generalized statistical mechanics for the complex behavior of these types of observables in complex environmental systems.…”

Section: Discussionmentioning

confidence: 99%

“…Of particular interest are superstatistical techniques to analyse and model the complexity inherent in environmental time series, such as rainfall, wind, surface temperature, and related quantities. Rapisarda et al [19] and Kantz et al [23] investigated superstatistical aspects of wind velocity fluctuations. Yalcin et al [24] did a data analysis of relevant surface temperature distributions on the earth, which is important if one wants to understand the effective statistical mechanics for thermodynamic devices (or local ecosystems) that are kept in the open air outside a constanttemperature environment.…”

Section: Introductionmentioning

confidence: 99%

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Superstatistical analysis of sea-level fluctuations

Rabassa

Beck

2015

Physica A: Statistical Mechanics and its Applications

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We perform a statistical analysis of measured time series of sea levels at various coastal locations in the UK, measured at time differences of 15 minutes over the past 20 years. When the astronomical tide and other deterministic components are removed from the record, a stochastic signal corresponding to the meteorological component remains, and this is well-described by a superstatistical model. We do various tests on the measured time series, and compare the data at 5 different UK locations. Overall the χ 2 -superstatistics is best suitable to describe the data, in particular when one looks at the dynamics of sea-level differences on short time scales.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Superstatistical analysis of sea-level fluctuations

Rabassa

Beck

2015

Physica A: Statistical Mechanics and its Applications

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“…In their work, they investigated the distribution of times and sound amplitudes larger than a fixed value. By using this kind of return interval analysis [35], they found Gaussian distributions in the amplitude for jazz, pop, and rock music, while nonGaussians emerge for classical pieces. Here, we directly investigate the amplitude distributions of songs of several genres without employing a threshold value as considered by Diodati and Piazza.…”

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confidence: 99%

Universal patterns in sound amplitudes of songs and music genres

et al. 2011

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We report a statistical analysis over more than eight thousand songs. Specifically, we investigate the probability distribution of the normalized sound amplitudes. Our findings seems to suggest a universal form of distribution which presents a good agreement with a one-parameter stretched Gaussian. We also argue that this parameter can give information on music complexity, and consequently it goes towards classifying songs as well as music genres. Additionally, we present statistical evidences that correlation aspects of the songs are directly related with the non-Gaussian nature of their sound amplitude distributions. In recent years, studies of complex systems have become widespread among the scientific community, specially in the statistical physics one [1][2][3][4][5]. Many of these investigations deal with data records ordered in time or space (i.e., time series), trying to extract some features, patterns or laws that may be present in the systems studied. This approach has been successfully applied to a variety of fields, from physics and astronomy [6] Music is a well known worldwide social phenomenon linked to the human cognitive habits, modes of consciousness as well as historical developments [14]. In the direction of music's social role, some authors investigated collective listening habits. For instance, Lambiotte and Ausloos [15] analyzed data from people music library finding audience groups with the size distribution following a power law. They also investigated correlations among these music groups, reporting non-trivial relations [16]. In another work, Silva et al.[17] studied the network structure of the song writers and the singers of Brazilian popular music (mpb). There is also an interest in the behavior of music sales [18] as well as in the success of musicians [19][20][21].Despite these cultural aspects, songs form a highly organized system presenting very complex structures and long-range correlations. All these features have attracted the attention of statistical physicists. In a seminal paper, Voss and Clarke [22] analyzed the power spectrum of radio stations and observed a 1/f noise like pattern. They also showed that the correlation can extend to longer or shorter time scales, depending on the music genre. Hsü and Hsü[23] investigated the changes of acoustic frequency in Bach's and Mozart's compositions, finding self-similarity and fractals structures. In contrast, they report no resemblance to fractal geometry [24] for modern music. Fractal structures have also been reported in the study of sequences of music notes [25], where Su and Wu [26] suggest that the multifractal spectrum can be used to distinguish different styles of music. In this brief literature review, we see that special attention was paid to the fractal structures of music, correlations and power spectrum analysis. However, much less attention has been paid to the understanding of the amplitude distribution. This last point has been noted by Diodati and Piazza[34]. In their work, they investigated the distribution of t...

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“…The effect of threshold choice has been shown, theoretically and using numerical simulation, to modify the return interval distribution, particularly in the case of short return intervals (Santhanam and Kantz, 2008). In the context of hydrologic data, the POT method is subject to a sensitivity to threshold choice, including a tendency for the estimates to become unstable at higher threshold levels due to natural sampling variability (Begueria, 2005).…”

Section: Datamentioning

confidence: 99%

Gridded return values of McArthur Forest Fire Danger Index across New South Wales

Louis¹

2014

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Return interval distribution of extreme events and long-term memory

Cited by 108 publications

References 42 publications

Superstatistical analysis of sea-level fluctuations

Superstatistical analysis of sea-level fluctuations

Universal patterns in sound amplitudes of songs and music genres

Gridded return values of McArthur Forest Fire Danger Index across New South Wales

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