Methods to Distinguish Between Polynomial and Exponential Tails

Castillo, Joan del; Daoudi, Jalila; Lockhart, Richard

doi:10.1111/sjos.12037

Cited by 17 publications

(30 citation statements)

References 18 publications

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“…It complements earlier ways to detect signs of heavy-tailedness such as the mean excess plot [11]. Further tests based on probabilistic features have been previously utilised in e.g., [12][13][14].…”

Section: Introductionmentioning

confidence: 84%

Distinguishing Log-Concavity from Heavy Tails

Asmussen

Lehtomaa

2017

Risks

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Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum X 1 + X 2 occur as result of a single big jump with heavy tails whereas X 1 , X 2 are of equal order of magnitude in the light-tailed case. The method is based on the ratio |X 1 − X 2 |/(X 1 + X 2 ), for which sharp asymptotic results are presented as well as a visual tool for distinguishing between the two cases. The study supplements modern non-parametric density estimation methods where log-concavity plays a main role, as well as heavy-tailed diagnostics such as the mean excess plot.

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Section: Introductionmentioning

confidence: 84%

Distinguishing Log-Concavity from Heavy Tails

Asmussen

Lehtomaa

2017

Risks

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“…To find the threshold from which the GPD model is appropriate, Castillo et al (2014) suggest use of the residual coefficient of variation, since it characterizes the distribution and does not depend on the scale parameter; see Gupta and Kirmani  be the ordered sample, so that x (1) ≤ x (2) ≤ · · · ≤ x (n) . Defining a CV-plot as the representation of the empirical coefficient of variation (cv n ) of the conditional exceedances, given by…”

Section: Real World Examplesmentioning

confidence: 99%

Likelihood inference for generalized Pareto distribution

Castillo

Serra

2015

Computational Statistics & Data Analysis

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“…For a given distribution the residual CV determines the type of the tail: CV = 1 for exponential tails, CV ≥ 1 for heavy tails and CV ≤ 1 for light tails [Del Castillo et al 2014].…”

Section: Background On Cv-plot: a Methods For Tail Classificationmentioning

confidence: 99%

“…Note that M (th) and V (th) are the theoretical counterparts of the empirical sd and x values obtained for a given sample. Based on the cv(th) estimator, one can iteratively draw the CV-plot that comprises a cv(th) value for each th [Del Castillo et al 2014]. The application of the CV-plot in the scope of EVT has not occurred until very recently.…”

Section: Empirical Residual CVmentioning

confidence: 99%

“…MBPTA-CV also specifically fits only values from the distribution of the tail in the data sample. To that end, MBPTA-CV builds on a recent tail-classification method for EVT projections -the CV-plot [Del Castillo et al 2014]. Overall, MBPTA-CV complies with all constraints related to the timinganalysis problem and applies EVT appropriately to deliver high-quality pWCET estimates.…”

Section: Introductionmentioning

confidence: 99%

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Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation

Abella

Padilla

Castillo

et al. 2017

ACM Trans. Des. Autom. Electron. Syst.

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115

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Extreme Value Theory (EVT) has been historically used in domains such as finance and hydrology to model worst-case events (e.g. major stock market incidences). EVT takes as input a sample of the distribution of the variable to model and fits the tail of that sample to either the Generalised Extreme Value (GEV) or the Generalised Pareto Distribution (GPD). Recently, EVT has become popular in real-time systems to derive worst-case execution time (WCET) estimates of programs. However, the application of EVT is not straightforward and requires a detailed analysis of, and customisation for, the particular problem at hand. In this paper we tailor the application of EVT to timing analysis. To that end (1) we analyse the response time of different hardware resources (e.g. cache memories) and identify those that may lead to radically different types of execution time distributions. (2) We show that one of these distributions, known as mixture distribution, causes problems in the use of EVT. In particular, mixture distributions challenge not only properly selecting GEV/GPD parameters (i.e., location, scale and shape), but also determining the size of the sample to ensure that enough tail values are passed to EVT and that only tail values are used by EVT to fit GEV/GPD. Failing to select these parameters has a negative impact on the quality of the derived WCET estimates. We tackle these problems, by (3) proposing MBPTA-CV, a new mixture-distribution aware, WCET-suited MBPTA method that builds upon recent EVT developments in other fields (e.g. finance) to automatically select the distribution parameters that best fit the maxima of the observed execution times. Our results on a simulation environment and a real board show that MBPTA-CV produces high-quality WCET estimates.

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Methods to Distinguish Between Polynomial and Exponential Tails

Cited by 17 publications

References 18 publications

Distinguishing Log-Concavity from Heavy Tails

Distinguishing Log-Concavity from Heavy Tails

Likelihood inference for generalized Pareto distribution

Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation

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