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Computer simulation study to determine normality or nonnormality on any given population of sampled data - statistical probability distribution
Digitized agricultural field boundary taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.
The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.
Models of varying complexity that simulate water vapor and clouds in the Tropical Tropopause Layer (TTL) show that including convection directly is essential to properly simulating the water vapor and cloud distribution. In boreal winter, for example, simulations without convection yield a water vapor distribution that is too uniform with longitude, as well as minimal cloud distributions. Two things are important for convective simulations. First, it is important to get the convective cloud top potential temperature correctly, since unrealistically high values (reaching above the cold point tropopause too frequently) will cause excessive hydration of the stratosphere. Second, one must capture the time variation as well, since hydration by convection depends on the local relative humidity (temperature), which has substantial variation on synoptic time scales in the TTL. This paper describes a method for obtaining high frequency (3-hourly) global convective cloud top distributions which can be used in trajectory models. The method uses rainfall thresholds, standard IR brightness temperatures, meteorological temperature analyses, and physically realistic and documented corrections IR brightness temperature corrections to derive cloud top altitudes and potential temperatures. The cloud top altitudes compare well with combined CLOUDSAT and CALIPSO data, both in time-averaged overall vertical and horizontal distributions and in individual cases (correlations of .65-.7). An important finding is that there is significant uncertainty (nearly .5 km) in evaluating the statistical distribution of convective cloud tops even using lidar. Deep convection whose tops are in regions of high relative humidity (such as much of the TTL), will cause clouds to form above the actual convection. It is often difficult to distinguish these clouds from the actual convective cloud due to the uncertainties of evaluating ice water content from lidar measurements. Comparison with models show that calculated cloud top altitudes are generally higher than those calculated by global analyses (e.g., MERRA). Interannual variability in the distribution of convective cloud top altitudes is also investigated.
The new and substantially upgraded version of the Table File System in MIDAS is presented as a scientific database system. MIDAS applications for performing database operations on tables are discussed, for instance, the exchange of the data to and from the TFS, the selection of objects, the uncertainty joins across tables, and the graphical representation of data. This upgraded version of the TFS is a full implementation of the binary table extension of the FITS format; in addition, it also supports arrays of strings. Different storage strategies for optimal access of very large data sets are implemented and are addressed in detail. As a simple relational database, the TFS may be used for the management of personal data files. This opens the way to intelligent pipeline processing of large amounts of data. One of the key features of the Table File System is to provide also an extensive set of tools for the analysis of the final results of a reduction process. Column operations using standard and special mathematical functions as well as statistical distributions can be carried out; commands for linear regression and model fitting using nonlinear least square methods and user-defined functions are available. Finally, statistical tests of hypothesis and multivariate methods can also operate on tables.
Bombardment with tightly focused electron beams has been suggested as a means of electrically disabling selected individual carbon-nanotubes (CNTs) in electronic devices. Evidence in support of the suggestion was obtained in an experiment in which a CNT field-effect transistor was disabled (see figure) by focusing a 1-keV electron beam on a CNT that served as the active channel of a field-effect transistor (FET). Such bombardment could be useful in the manufacture of nonvolatile-memory circuits containing CNT FETs. Ultimately, in order to obtain the best electronic performances in CNT FETs and other electronic devices, it will be necessary to fabricate the devices such that each one contains only a single CNT as an active element. At present, this is difficult because there is no way to grow a single CNT at a specific location and with a specific orientation. Instead, the common practice is to build CNTs into electronic devices by relying on spatial distribution to bridge contacts. This practice results in some devices containing no CNTs and some devices containing more than one CNT. Thus, CNT FETs have statistically distributed electronic characteristics (including switching voltages, gains, and mixtures of metallic and semiconducting CNTs). According to the suggestion, by using a 1-keV electron beam (e.g., a beam from a scanning electron microscope), a particular nanotube could be rendered electrically dysfunctional. This procedure could be repeated as many times as necessary on different CNTs in a device until all of the excess CNTs in the device had been disabled, leaving only one CNT as an active element (e.g., as FET channel). The physical mechanism through which a CNT becomes electrically disabled is not yet understood. On one hand, data in the literature show that electron kinetic energy >86 keV is needed to cause displacement damage in a CNT. On the other hand, inasmuch as a 1-keV beam focused on a small spot (typically a few tens of nanometers wide) deposits a significant amount of energy in a small volume, the energy density may suffice to thermally induce structural and/or electronic changes that disable the CNT. Research may be warranted to investigate this effect in detail.
The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.
Design loads are presented for the General Electric MOD-SA wind turbine. The MOD-SA system consists of a 400 ft. diameter, upwind, two-bladed, teetered rotor connected to a 7.3 mW variable-speed generator. Fatigue loads are specified in the form of histograms for the 30 year life of the machine, while limit (or maximum) loads have been derived from transient dynamic analysis at critical operating conditions. Loads prediction was accomplished using state of the art aeroelastic analyses developed at General Electric. Features of the primary predictive tool - the Transient Rotor Analysis Code (TRAC) are described in the paper. Key to the load predictions are the following wind models: (1) yearly mean wind distribution; (2) mean wind variations during operation; (3) number of start/shutdown cycles; (4) spatially large gusts; and (5) spatially small gusts (local turbulence). The methods used to develop statistical distributions from load calculations represent an extension of procedures used in past wind programs and are believed to be a significant contribution to Wind Turbine Generator analysis. Test/theory correlations are presented to demonstrate code load predictive capability and to support the wind models used in the analysis. In addition MOD-5A loads are compared with those of existing machines. The MOD-5A design was performed by the General Electric Company, Advanced Energy Program Department, under Contract DEN3-153 with NASA Lewis Research Center and sponsored by the Department of Energy.
This report investigates two of the most common modes of localized failures, namely, periodic fiber-bridged matrix cracks and transverse matrix cracks. A modification of Daniels' bundle theory is combined with Weibull's weakest link theory to model the statistical distribution of the periodic matrix cracking strength for an individual layer. Results of the model predictions are compared with experimental data from the open literature. Extensions to the model are made to account for possible imperfections within the layer (i.e., nonuniform fiber lengths, irregular crack spacing, and degraded in-situ fiber properties), and the results of these studies are presented. A generalized shear-lag analysis is derived which is capable of modeling the development of transverse matrix cracks in material systems having a general multilayer configuration and under states of full in-plane load. A method for computing the effective elastic properties for the damaged layer at the global level is detailed based upon the solution for the effects of the damage at the local level. This methodology is general in nature and is therefore also applicable to (0(sub m)/90(sub n))(sub s) systems. The characteristic stress-strain response for more general cases is shown to be qualitatively correct (experimental data is not available for a quantitative evaluation), and the damage evolution is recorded in terms of the matrix crack density as a function of the applied strain. Probabilistic effects are introduced to account for the statistical nature of the material strengths, thus allowing cumulative distribution curves for the probability of failure to be generated for each of the example laminates. Additionally, Oh and Finney's classic work on fracture location in brittle materials is extended and combined with the shear-lag analysis. The result is an analytical form for predicting the probability density function for the location of the next transverse crack occurrence within a crack bounded region. The results of this study verified qualitatively the validity of assuming a uniform crack spacing (as was done in the shear-lag model).
The diffusion equation which describes the evolution of the average one particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicity evaluated for a strongly turbulent unmagnetized plasma.
Electrostatic Discharge (ESD) induced by the accumulation of charge in the space environment is known to cause spacecraft anomalies and failures. While it is critical to estimate the worst-case expected ESD, sensitive radar instruments can be impacted by high rates of occurrence of very small ESD. To estimate the correct extreme behavior, it is important to select the correct extreme value distribution for extrapolation of test results limited in time and sensitivity. Quantile-quantile (Q-Q) analysis is used to compare electron beam-induced ESD test data to several statistical distributions used in the published literature. The best-fit distribution is shown to vary from between tests on different materials; however, it is clear that power law distributions are not good approximations for low amplitude events. Q-Q analysis is a convenient graphical method for evaluating multiple theoretical extreme-value distributions simultaneously.
A method to estimate the frequency of transmission overhauls is presented. This method is based on the two-parameter Weibull statistical distribution for component life. A second method is presented to estimate the number of replacement components needed to support the transmission overhaul pattern. The second method is based on renewal theory. Confidence statistics are applied with both methods to improve the statistical estimate of sample behavior. A transmission example is also presented to illustrate the use of the methods. Transmission overhaul frequency and component replacement calculations are included in the example.
A method to estimate the frequency of transmission overhauls is presented. This method is based on the two-parameter Weibull statistical distribution for component life. A second method is presented to estimate the number of replacement components needed to support the transmission overhaul pattern. The second method is based on renewal theory. Confidence statistics are applied with both methods to improve the statistical estimate of sample behavior. A transmission example is also presented to illustrate the use of the methods. Transmission overhaul frequency and component replacement calculations are included in the example.
The default method of dealing with missing data in statistical analyses is to only use the complete observations (complete case analysis), which can lead to unexpected bias when data do not meet the assumption of missing completely at random (MCAR). For the assumption of MCAR to be met, missingness cannot be related to either the observed or unobserved variables. A less stringent assumption, missing at random (MAR), requires that missingness not be associated with the value of the missing variable itself, but can be associated with the other observed variables. When data are truly MAR as opposed to MCAR, the default complete case analysis method can lead to biased results. There are statistical options available to adjust for data that are MAR, including multiple imputation (MI) which is consistent and efficient at estimating effects. Multiple imputation uses informing variables to determine statistical distributions for each piece of missing data. Then multiple datasets are created by randomly drawing on the distributions for each piece of missing data. Since MI is efficient, only a limited number, usually less than 20, of imputed datasets are required to get stable estimates. Each imputed dataset is analyzed using standard statistical techniques, and then results are combined to get overall estimates of effect. A simulation study will be demonstrated to show the results of using the default complete case analysis, and MI in a linear regression of MCAR and MAR simulated data. Further, MI was successfully applied to the association study of CO2 levels and headaches when initial analysis showed there may be an underlying association between missing CO2 levels and reported headaches. Through MI, we were able to show that there is a strong association between average CO2 levels and the risk of headaches. Each unit increase in CO2 (mmHg) resulted in a doubling in the odds of reported headaches.
Data collected from the GARP Atlantic Tropical Experiment (GATE) was examined. The data were collected from 10,000 grid points arranged as a 100 x 100 array; each grid covered a 4 square km area. The amount of rainfall was measured every 15 minutes during the experiment periods using c-band radars. Two types of analyses were performed on the data: analysis of diurnal variation was done on each of grid points based on the rainfall averages at noon and at midnight, and time series analysis on selected grid points based on the hourly averages of rainfall. Since there are no known distribution model which best describes the rainfall amount, nonparametric methods were used to examine the diurnal variation. Kolmogorov-Smirnov test was used to test if the rainfalls at noon and at midnight have the same statistical distribution. Wilcoxon signed-rank test was used to test if the noon rainfall is heavier than, equal to, or lighter than the midnight rainfall. These tests were done on each of the 10,000 grid points at which the data are available.
A PC-based near-real time implementation of a two-channel maximum-likelihood classifier is described. The statistical distribution of the reflectance characteristics of ice, frost, and water formation on spray-on-foam-insulation, which covers the External Tank surface of the Space Shuttle, is acquired. The classification technique is based on these statistics. The computer, set in either a training or a classifying mode, learns the statistics of the various classes, or produces a color-coded image denoting the respective categories of classification. The classified results are memory-mapped for efficiency. The speed of the classification process is only limited by the speed of the digital frame grabber and the software that interfaces the frame grabber to the monitor. The process took 4 seconds for a 512 x 480 pixel image.
Effective flame speeds of free turbulent flames were measured by photographic, ionization-gap, and photomultiplier-tube methods, and were found to have a statistical distribution attributed to the nature of the turbulent field. The effective turbulent flame speeds for the free flame were less than those previously measured for flames stabilized on nozzle burners, Bunsen burners, and bluff bodies. The statistical spread of the effective turbulent flame speeds was markedly wider in the lean and rich fuel-air-ratio regions, which might be attributed to the greater sensitivity of laminar flame speed to flame temperature in those regions. Values calculated from the turbulent free-flame-speed analysis proposed by Tucker apparently form upper limits for the statistical spread of free-flame-speed data. Hot-wire anemometer measurements of the longitudinal velocity fluctuation intensity and longitudinal correlation coefficient were made and were employed in the comparison of data and in the theoretical calculation of turbulent flame speed.
Because CFC 113, an ozone depleting chemical (ODC), can no longer be produced, alternative bearing cleaning methods must be studied. The objective of this work was to study the effect of the new cleaning methods on lubricant lifetime using a vacuum bearing simulator (spiral orbit rolling contact tribometer). Four alternative cleaning methods were studied: ultra-violet (UV) ozone, aqueous levigated alumina slurry (ALAS), super critical fluid (SCF) CO2 and aqueous Brulin 815GD. Baseline tests were done using CFC 113. Test conditions were the following: a vacuum of at least 1.3 x 10(exp -6) Pa, 440C steel components, a rotational speed of 10 RPM, a lubricant charge of between 60-75 micrograms, a perfluoropolyalkylether lubricant (Z-25), and a load of 200N (44.6 lbs., a mean Hertzian stress of 1.5 GPa). Normalized lubricant lifetime was determined by dividing the total number of ball orbits by the amount of lubricant. The failure condition was a friction coefficient of 0.38. Post-test XPS analysis was also performed, showing slight variations in post-cleaning surface chemistry. Statistical analysis of the resultant data was conducted and it was determined that the data sets were most directly comparable when subjected to a natural log transformation. The natural log life (NL-Life) data for each cleaning method were reasonably normally (statistically) distributed and yielded standard deviations that were not significantly different among the five cleaning methods investigated. This made comparison of their NL-Life means very straightforward using a Bonferroni multiple comparison of means procedure. This procedure showed that the ALAS, UV-ozone and CFC 113 methods were not statistically significantly different from one another with respect to mean NL-Life. It also found that the SCF CO2 method yielded a significantly higher mean NL-Life than the mean NL-Lives of the ALAS, UV-ozone and CFC 113 methods. It also determined that the aqueous Brulin 815GD method yielded a mean NL-Life that was statistically significantly higher than the mean NL-Lives of each of the other four methods. Baseline tests using CFC 113 cleaned parts yielded a mean NL-Life 3.62 orbits/micro-g. ALAS and UV-ozone yielded similar mean NL-Life (3.31 orbits/mg and 3.33 orbits/micro-g, respectively). SCF CO2, gave a mean NL-Life of 4.08 orbits/mg and aqueous Brulin 8l5GD data yielded the longest mean NL-Life (4.66 orbits/micro-g).