Parameter Estimation for the Truncated Pareto Distribution

Aban, Inmaculada; Meerschaert, Mark M.; Panorska, Anna K.

doi:10.1198/016214505000000411

Cited by 247 publications

(255 citation statements)

References 44 publications

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“…The same algorithm may terminate in linear time if the input is already sorted to begin with, but may require quadratic time if the input is sorted in the opposite order. The same phenomena may happen when evaluating complete systems: they may perform well for one workload, but not for another 1 . To demonstrate the importance of workloads we therefore describe three examples in which the workload makes a large difference to the evaluation results.…”

Section: The Importance Of Workloadsmentioning

confidence: 97%

“…To understand it, let us compare the tail of a heavy-tailed distribution with the tail of an exponential distribution. With an exponential distribution, the probability of sampling a value larger than, say, 100 times the mean is e −100 , which is totally negligible 1 . But for a Pareto distribution with a = 2, this probability is 1/40, 000: one in every 40,000 samples will be bigger than 100 times the mean.…”

Section: Power-law Tailsmentioning

confidence: 99%

“…However, the observed shape depends on the resolution of the observation. An example is given in Figure 3.4 1 . This shows a distribution of memory usage, where the maximal possible value is 32 MB.…”

Section: Shapes Of Distributionsmentioning

confidence: 99%

“…In particular, we can assign them a value according to Zipf's law. The most useful connection is given a value of 1. the next most useful has a value of 1 2 , the third 1 3 , and so on. The sum of all these values is then on the order of log n, and the total value of the network is only n log n, not n 2 [90].…”

Section: Connection Box: the Value Of A Networkmentioning

confidence: 99%

“…The distribution in question is the distribution of job runtimes from the HPC2N Linux cluster. This dataset contains information about more than a half-million jobs submitted over a period of 3 1 2 years (we use the full log here, not the cleaned version). As seen in the figure, there are a number of prominent modes where very many jobs had similar runtimes.…”

Section: Modeling With a Mixture Of Gaussiansmentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

184

128

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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Section: The Importance Of Workloadsmentioning

confidence: 97%

Section: Power-law Tailsmentioning

confidence: 99%

Section: Shapes Of Distributionsmentioning

confidence: 99%

Section: Connection Box: the Value Of A Networkmentioning

confidence: 99%

Section: Modeling With a Mixture Of Gaussiansmentioning

confidence: 99%

See 3 more Smart Citations

Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

184

128

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Substrate size and heterogeneity control anomalous transport in small streams

Aubeneau

Hanrahan

Bolster

et al. 2014

Geophysical Research Letters

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In alluvial systems, substrate characteristics play a critical role in slowing downstream transport of both water and solutes. We present results from solute injection experiments testing the influence of sediment size (pea gravel versus coarse gravel) and heterogeneity (alternating sections versus well-mixed reaches) on solute transport dynamics in four experimental streams at the Notre Dame Linked Experimental Ecosystem Facility. The stream with pea gravel resulted in more long-term retention than the stream with coarse gravel, whereas both streams with heterogeneous substrate (alternated and mixed) fell between with similar late-time scaling. Inverse modeling of solute breakthrough curves suggested that residence times were distributed according to a truncated power law. While conservative solute transport in all four streams was anomalous, truncation times were influenced by sediment size, with the smaller pea gravel exhibiting a later truncation time than the coarse gravel, and the two streams with heterogeneous substrate having an intermediate cutoff. These results uniquely associate transport scaling with substrate characteristics in fluvial systems, revealing truncation time scales that had been previously predicted but not observed and quantified in field conditions. Because both benthic (i.e., substrate-water interface) and subsurface hyporheic regions are known biogeochemical hot spots, relating physical characteristics to the macroscopic transport behavior could be crucial to improve our estimates of solute export from fluvial systems.

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Numerical simulation of large‐scale bed load particle tracer advection‐dispersion in rivers with free bars

et al. 2017

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Asymptotic characteristics of the transport of bed load tracer particles in rivers have been described by advection‐dispersion equations. Here we perform numerical simulations designed to study the role of free bars, and more specifically single‐row alternate bars, on streamwise tracer particle dispersion. In treating the conservation of tracer particle mass, we use two alternative formulations for the Exner equation of sediment mass conservation: the flux‐based formulation, in which bed elevation varies with the divergence of the bed load transport rate, and the entrainment‐based formulation, in which bed elevation changes with the net deposition rate. Under the condition of no net bed aggradation/degradation, a 1‐D flux‐based deterministic model that does not describe free bars yields no streamwise dispersion. The entrainment‐based 1‐D formulation, on the other hand, models stochasticity via the probability density function (PDF) of particle step length, and as a result does show tracer dispersion. When the formulation is generalized to 2‐D to include free alternate bars, however, both models yield almost identical asymptotic advection‐dispersion characteristics, in which streamwise dispersion is dominated by randomness inherent in free bar morphodynamics. This randomness can result in a heavy‐tailed PDF of waiting time. In addition, migrating bars may constrain the travel distance through temporary burial, causing a thin‐tailed PDF of travel distance. The superdiffusive character of streamwise particle dispersion predicted by the model is attributable to the interaction of these two effects.

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Parameter Estimation for the Truncated Pareto Distribution

Cited by 247 publications

References 44 publications

Workload Modeling for Computer Systems Performance Evaluation

Workload Modeling for Computer Systems Performance Evaluation

Substrate size and heterogeneity control anomalous transport in small streams

Numerical simulation of large‐scale bed load particle tracer advection‐dispersion in rivers with free bars

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