Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas
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George Livadiotis↗
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RFI Statistical Distribution and Missed Detection in Aquarius Radiometer Measurements
Aquarius is an microwave active/passive sensor whose main goal is to globally estimate sea surface salinity from space. Two instruments, a radar scatterometer and a radiometer, operate at L-band observing the same surface footprint almost simultaneously. The sensitivity to sea surface salinity (SSS) is given by the radiometer, while the scatterometer measurements provide a correction for sea surface roughness. Although the primary objective is the measurement of SSS, the instrument combination operates continuously, acquiring data over land and sea ice as well. Radio Frequency Interference (RFI) can occur in both the radiometer and the scatterometer bands of operation, and for this reason detection and mitigation of RFI was included in the data processing of both active and passive instruments. This paper will focus on the RFI processing for the Aquarius radiometer only and provide an update on the efforts to reduce the amount of missed RFI detection.
RFI↗
Statistical Distribution of Gear Surface Fatigue Lives at High Reliability
The reliability of gears is important for a wide variety of applications, and the gearing community has a desire for better prediction of fatigue life at very high reliability. To improve predictions, a set of 950 NASA-conducted gear surface fatigue test results were gathered, pooled together using the general standardized Weibull variate, and then fit to a Weibull three-parameter distribution. An iterative fitting method was developed and then applied to the gear fatigue data to determine the values of the distribution parameters. Additional analyses were done using bearing and gear data that demonstrate a trend of increasing minimum life coefficient as correlated to the timeframe of the fatigue testing, and material cleanliness is proposed as a primary explanation for such correlation. It is noted that this observed trend supports published findings from analytical modeling and experimental studies that improvements to material cleanliness improves minimum fatigue life. Further use and study of the three-parameter Weibull distribution is recommended as a tool to quantify fatigue life most accurately in the high reliability regime.
gear↗
The beta distribution: A statistical model for world cloud cover
Much work has been performed in developing empirical global cloud cover models. This investigation was made to determine an underlying theoretical statistical distribution to represent worldwide cloud cover. The beta distribution with probability density function is given to represent the variability of this random variable. It is shown that the beta distribution possesses the versatile statistical characteristics necessary to assume the wide variety of shapes exhibited by cloud cover. A total of 160 representative empirical cloud cover distributions were investigated and the conclusion was reached that this study provides sufficient statical evidence to accept the beta probability distribution as the underlying model for world cloud cover.
Falls, L. W.↗
The beta distribution - A statistical model for world cloud cover
A statistical distribution representing worldwide cloud cover is obtained as a basis for an empirical global cloud cover model incorporating some 29 regions of the globe which are of interest to NASA's Skylab Program. A total of 160 representative empirical cloud cover distributions were investigated with the conclusion that the beta probability distribution is an adequate model for world cloud cover.
Falls, L. W.↗
Utilization of a priori information by means of mathematical programming in the statistical interpretation of measured distributions
Statistical interpretation of measurement distributions - a priori information
STATISTICS↗
The QCD phase diagram and statistics friendly distributions
The preliminary STAR data for proton cumulants for central collisions at \sqrt{s}=7.7 GeV are consistent with a two-component proton multiplicity distribution. We show that this two-component distribution is statistics friendly in that factorial cumulants of surprisingly high orders may be extracted with a relatively small number of events. As a consequence the two-component model can be tested and verified right now with the presently available STAR data from the first phase of the RHIC beam energy scan.
Koch, Volker↗
Spectroscopic Study of Solar Transition Region Oscillations in the Quiet-Sun Observed By IRIS Using Si IV Spectral Line
In the present paper, we use Si IV 1393.755 Å spectral line observed by the Interface Region Imaging Spectrograph (IRIS) in the quiet-Sun to determine physical nature of the solar transition region (TR) oscillations. We analyze the properties of these oscillations using wavelet tools (e.g., power, cross-power, coherence, and phase difference) along with the stringent noise model (i.e., power-law + constant). We estimate the period of the intensity and Doppler velocity oscillations at each chosen location in the quiet-Sun (QS) and quantify the distribution of the statistically significant power and associated periods in one bright and two dark regions. In the bright TR region, the mean periods in intensity and velocity are 7 min, and 8 min respectively. In the dark region, the mean periods in intensity and velocity are 7 min, and 5.4 min respectively. We also estimate the phase difference between the intensity and Doppler velocity oscillations at each location. The statistical distribution of phase difference is estimated, which peaks at -119°± 13°, 33°± 10°, 102°± 10° in the bright region, while at -153°± 13°, 6°± 20°, 151°± 10° in the dark region. The statistical distribution reveals that the oscillations are caused by propagating slow magnetoacoustic waves encountered with the TR. Some of these locations may also be associated with the standing slow waves. Even, in the given time domain, several locations exhibit presence of both propagating and standing oscillations at different frequencies.
Sun: oscillations↗
Spectroscopic Study of Solar Transition Region Oscillations in the Quiet-Sun Observed By IRIS Using the Si IV Spectral Line
In this paper, we use the Si IV 1393.755 Å spectral line observed by the Interface Region Imaging Spectrograph (IRIS) in the quiet-Sun (QS) to determine the physical nature of the solar transition region (TR) oscillations. We analyse the properties of these oscillations using wavelet tools (e.g. power, cross-power, coherence, and phase difference) along with the stringent noise model (i.e. power law + constant). We estimate the period of the intensity and Doppler velocity oscillations at each chosen location in the QS and quantify the distribution of the statistically significant power and associated periods in one bright region and two dark regions. In the bright TR region, the mean periods in intensity and velocity are 7 min and 8 min, respectively. In the dark regions, the mean periods in intensity and velocity are 7 min and 5.4 min, respectively. We also estimate the phase difference between the intensity and Doppler velocity oscillations at each location. The statistical distribution of the phase difference is estimated, which peaks at −119° ± 13°, 33° ± 10°, 102° ± 10° in the bright region and at −153° ± 13°, 6° ± 20°, 151° ± 10° in the dark regions. The statistical distribution reveals that the oscillations are caused by propagating slow magneto-acoustic waves encountered with the TR. Some of these locations may also be associated with standing slow waves. Moreover, in the given time domain, several locations exhibit the presence of both propagating and standing oscillations at different frequencies.
MHD – Sun: oscillations↗
Characterization of spatial statistics of distributed targets in SAR data
A statistical approach to the analysis of spatial statistics in polarimetric multifrequency SAR data, which is aimed at extracting the intrinsic variability of the target by removing variability from other sources, is presented. An image model, which takes into account three sources of spatial variability, namely, image speckle, system noise, and the intrinsic spatial variability of the target or texture, is described. It is shown that the presence of texture increases the image variance-to-mean square ratio and introduces deviations of the image autocovariance function from the expected SAR system response. The approach is exemplified by sea-ice SAR imagery acquired by the Jet Propulsion Laboratory three-frequency polarimetric airborne SAR. Data obtained indicate that, for different sea-ice types, the spatial statistics seem to vary more across frequency than across polarization and the observed differences increase in magnitude with decreasing frequency.
Rignot, E.↗
Performance Comparison of Circular and Spherical Error Probable Estimators
This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.
97 MATHEMATICS AND COMPUTING↗
Qualitative aspects of asteroid statistics.
Distribution asteroids in space studied by computer analysis from selected plots of orbital elements
PLOTTING↗
Joint aircraft loading/structure response statistics of time to service crack initiation
A reliability analysis for predicting the statistical distribution of time to fatigue crack initiation for aircraft structures in service is presented. The present analysis utilizes the statistical data of the specimen fatigue tests, the full-scale structure tests, and the statistical dispersion of aircraft service loads. The statistical distribution of the time to fatigue crack initiation of the full-scale structure under laboratory loading spectrum is assumed to be Weibull. The service loads for gust turbulences are modeled as Poisson processes for transport-type aircraft, while the maneuver loads are modeled as compound Poisson processes for fighter and training aircraft. It is found that the statistical distribution of time to fatigue crack initiation for aircraft structures in service is not Weibull and that the prediction on the basis of the Weibull distribution is unconservative, in particular in the early service time.
Yang, J.-N.↗
Nearest neighbour distributions: New statistical measures for cosmological clustering
ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.
79 ASTRONOMY AND ASTROPHYSICS↗
Bayesian estimation of crack initiation times from service data
Lockheed C-130 Hercules aircraft have during their service life been periodically inspected and growing cracks around rivet holes were recorded. This record has recently been used to determine the statistical distributions of crack initiation times and the distribution of initial crack sizes. When crack initiation times are calculated from such cracks, by backward extrapolation of the growth relation, the resulting distribution of crack initiation times will indicate a preponderance of short times to crack initiation. If however, such distributions are combined with the reliability of the inspection procedure, the statistical distribution of missed initiation times can be estimated. The method used is based on Bayes theorem which permits the calculation of the 'prior' distribution (initiation times before inspection) from a knowledge of the 'posterior' distribution (initiation times obtained from the inspection) and a 'likelihood function' (reliability of the inspection) procedure. The results indicate that during an early inspection a large percentage of initiation times will be missed and that the fraction of located initiation times increases during later inspections.
Heller, R. A.↗
Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.
97 MATHEMATICS AND COMPUTING↗
Quantifying Graph Uncertainty from Communication Data
Graphs are a widely used abstraction for representing a variety of important real-world problems including emulating cyber networks for situational awareness, or studying social networks to understand human interactions or pandemic spread. Communication data is often converted into graphs to help understand social and technical patterns in the underlying communication data. However, prior to this project, little work had been performed analyzing how best to develop graphs from such data. Thus, many critical, national security problems were being performed against graph representations of questionable quality. Herein, we describe our analyses that were precursors to our final statistically grounded technique for creating static graph snapshots from a stream of communication events. The first analyzes the statistical distribution properties of a variety of real-world communication datasets generally fit best by Pareto, log normal, and extreme value distributions. The second derives graph properties that can be estimated given the expected statistical distribution for communication events and the communication interval to be viewed node observability, edge observability, and expected accuracy of node degree. Unfortunately, as that final process is under review for publication, we can't publish it here at this time.
97 MATHEMATICS AND COMPUTING↗