The Three Sigma Rule

Pukelsheim, Friedrich

doi:10.2307/2684253

Cited by 372 publications

(280 citation statements)

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“…The supports for the two-sided random disturbance were chosen to be symmetric around zero since we expect the random errors to be mean zero. We follow the 3r rule developed by Pukelsheim (1994) to choose the largest and smallest error support points. Since r is unknown we use the consistent estimatorr ¼ 0:144 from OLS estimation of Eq.…”

Section: Gme Resultsmentioning

confidence: 99%

Efficient frontier estimation: a maximum entropy approach

2008

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Section: Gme Resultsmentioning

confidence: 99%

Efficient frontier estimation: a maximum entropy approach

2008

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“…Moreover, the runtimes of both CGAR and CGAR_OS increase significantly when EPS.d exceeds 60 km or when EPS.t exceeds 8 days. This result can be explained by the three-sigma rule in a Gaussian distribution (Pukelsheim 1994). In the data generator, the spatial standard deviation γ and the temporal standard deviation ε of the Gaussian distribution on the spots are set to 25 km and 5 days, respectively.…”

Section: Methodsmentioning

confidence: 92%

A new method for discovering behavior patterns among animal movements

Wang

Luo

Takekawa

et al. 2015

International Journal of Geographical Information Science

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Advanced satellite tracking technologies enable biologists to track animal movements at fine spatial and temporal scales. The resultant data present opportunities and challenges for understanding animal behavioral mechanisms. In this paper, we develop a new method to elucidate animal movement patterns from tracking data. Here, we propose the notion of continuous behavior patterns as a concise representation of popular migration routes and underlying sequential behaviors during migration. Each stage in the pattern is characterized in terms of space (i.e., the places traversed during movements) and time (i.e. the time spent in those places); that is, the behavioral state corresponding to a stage is inferred according to the spatiotemporal and sequential context. Hence, the pattern may be interpreted predictably. We develop a candidate generation and refinement framework to derive all continuous behavior patterns from raw trajectories. In the framework, we first define the representative spots to denote the underlying potential behavioral states that are extracted from individual trajectories according to the similarity of relaxed continuous locations in certain distinct time intervals. We determine the common behaviors of multiple individuals according to the spatiotemporal proximity of representative spots and apply a projection-based extension approach to generate candidate sequential behavior sequences as candidate patterns. Finally, the candidate generation procedure is combined with a refinement procedure to derive continuous behavior patterns. We apply an ordered processing strategy to accelerate candidate refinement. The proposed patterns and discovery framework are evaluated through conceptual experiments on both real GPS-tracking and large synthetic datasets.

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“…We also compared the 3-sigma, which is defined by the mean + 3x standard deviation (SD), as a value representing the "near-maximum" error [13]. Under the Gaussian distribution, an error that exceeds the 3-sigma is experienced at a chance of 0.13 %.…”

Section: Discussionmentioning

confidence: 99%