On the histogram as a density estimator:L 2 theory

Freedman, David A.; Diaconis, Persi

doi:10.1007/bf01025868

Cited by 1,195 publications

(744 citation statements)

References 9 publications

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“…Tertiary γ′ analysis was carried out via the same method but using higher resolution STEM micrographs. The equivalent circular diameters were binned using the Freedman-Diaconis method [14] and fitted with lognormal functions, given in Eq. [3], using Igor Pro (WaveMetrics, Lake Oswego, OR).…”

Section: Methodsmentioning

confidence: 99%

Gamma Prime Precipitate Evolution During Aging of a Model Nickel-Based Superalloy

Goodfellow

Galindo-Nava

Christofidou

et al. 2017

Metall Mater Trans A

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The microstructural stability of nickel-based superalloys is critical for maintaining alloy performance during service in gas turbine engines. In this study, the precipitate evolution in a model polycrystalline Ni-based superalloy during aging to 1000 hours has been studied via transmission electron microscopy, atom probe tomography, and neutron diffraction. Variations in phase composition and precipitate morphology, size, and volume fraction were observed during aging, while the constrained lattice misfit remained constant at approximately zero. The experimental composition of the γ matrix phase was consistent with thermodynamic equilibrium predictions, while significant differences were identified between the experimental and predicted results from the γ′ phase. These results have implications for the evolution of mechanical properties in service and their prediction using modeling methods.

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Section: Methodsmentioning

confidence: 99%

Gamma Prime Precipitate Evolution During Aging of a Model Nickel-Based Superalloy

Goodfellow

Galindo-Nava

Christofidou

et al. 2017

Metall Mater Trans A

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“…The histograms of incident duration frequency distributions for different road types and incident types on weekdays are shown in Figure 5.10. The Freedman-Diaconis rule (Freedman and Diaconis, 1981) was used to select the size of the bins of the histogram.…”

Section: Figure 58 Crash Duration By Day Of Week and Different Roadmentioning

confidence: 99%

Modelling the impact of traffic incidents on travel time reliability

Hojati

Ferreira

Washington

et al. 2016

Transportation Research Part C: Emerging Technologies

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Assessing and prioritising cost-effective strategies to mitigate the impacts of non-recurrent congestion on major roads, due to traffic incidents, represents a significant challenge for road network managers. In addition, traffic incidents impose significant unexpected changes in the travel time of travellers.Travel Time Reliability (TTR) has become one of the most important indicators of transport performance. In this regard, the impact of traffic incidents on TTR is crucial for both operators and travellers. An extensive literature review indicated that there is a lack of relevant research in this area. To address and improve the knowledge in this area, this thesis established a four-stage logical framework to achieve the main objective of this research. The research was aimed at modelling traffic incident impacts and quantifying the effects of traffic incidents on TTR on freeways.Based on historical data from an 'integrated database', a robust methodology to identify recurrent and non-recurrent congestion and to recognise traffic incident related congestion was proposed. Further, a number of attributes relating to traffic incidents and traffic measures for both recurrent and non-recurrent congestion were extracted to quantify the impacts of traffic incidents, including incident duration and buffer time as a measure of TTR. This facilitated insight into the factors that affect these two important impacts of incidents.Extra Buffer Time was defined to calculate the extra travel time caused by traffic incidents.This reliability measure indicates how much time is required by travellers to arrive at their destination on time with 95% certainty, in the case of an incident, over and above the travel time that would have been taken under recurrent conditions. The Extra Buffer Time Index (EBTI) was calculated to show the ratio of changes in TTR in the case of an incident.A hazard-based duration modelling approach was considered to model incident duration.Parametric accelerated failure time survival models were developed to consider heterogeneity across duration in the hazard function and in the explanatory variables. In addition, a new approach was proposed to model EBTI using a Tobit model to understand the factors affecting EBTI. Moreover, this research considered both fixed and random parameters to capture unobserved heterogeneity across data. A validation process was performed to assess the level of accuracy of the results of the prediction models.ii An integrated database was established using historical data from different sources including 12 months of incident data, 18 months of traffic data, and weather data for the same period for an Australian freeway network. The results of the analysis showed that the significant variables affecting incident duration include characteristics of the incidents (severity, type, injury, medical required, etc.), infrastructure characteristics (shoulder availability), location, time of day, and traffic characteristics. Moreover, the findings revealed no significant effect...

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“…6 in Rickman et al (2001) but for real comets. In the histograms, we adopt Poisson statistics (σ = √ n) to compute the error bars -applying the approximation given by Gehrels (1986) when n < 21, σ ∼ 1 + √ 0.75 + nand the bin width has been found using the Freedman-Diaconis rule (Freedman & Diaconis 1981), i.e. 2 IQR n −1/3 , where IQR is the interquartile range and n is the number of data points.…”

Section: Introductionmentioning

confidence: 99%

Evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects: Avoiding a trans-Plutonian planet or just plain bias?

Marcos

2017

Monthly Notices of the Royal Astronomical Society: Letters

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It is a well-known fact that the presence of a massive perturber interacting with a population of minor bodies following very eccentric orbits can strongly affect the distribution of their nodal distances. The details of this process have been explored numerically and its outcome confirmed observationally in the case of Jupiter, where a bimodal distribution of nodal distances of comets has been found. Here, we show evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects (ETNOs) in the form of a previously unnoticed correlation between nodal distance and orbital inclination. This proposed correlation is unlikely to be the result of observational bias as data for both large semimajor axis Centaurs and comets fit well into the pattern found for the ETNOs, and all these populations are subjected to similar background perturbations when moving well away from the influence of the giant planets. The correlation found is better understood if these objects tend to avoid a putative planet with semimajor axis in the range of 300-400 au.

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On the histogram as a density estimator:L 2 theory

Cited by 1,195 publications

References 9 publications

Gamma Prime Precipitate Evolution During Aging of a Model Nickel-Based Superalloy

Gamma Prime Precipitate Evolution During Aging of a Model Nickel-Based Superalloy

Modelling the impact of traffic incidents on travel time reliability

Evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects: Avoiding a trans-Plutonian planet or just plain bias?

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