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NASA NTRS1976

Characterizations of linear sufficient statistics

A necessary and sufficient condition is developed such that there exists a continous linear sufficient statistic T for a dominated collection of totally finite measures defined on the Borel field generated by the open sets of a Banach space X. In particular, corollary necessary and sufficient conditions are given so that there exists a rank K linear sufficient statistic T for any finite collection of probability measures having n-variate normal densities. In this case a simple calculation, involving only the population means and covariances, determines the smallest integer K for which there exists a rank K linear sufficient statistic T (as well as an associated statistic T itself).

Peters, B. C., Jr.↗

NASA NTRS1978

Statistical models of summer rainshowers derived from fine-scale radar observations

A statistical modeling of rain cell characteristics is presented; the modeling is based on high-resolution radar measurements of the cell structure. The analysis of the fine-scale three-dimensional structure of summer rainshowers in the mid-Atlantic region leads to statistical descriptions of the rain cells in terms of a variety of physical cell parameters. Core reflectivity profiles, contour area, and altitude extent of the cells have been determined along with the frequency of occurrence for various storm classes and categories. The statistical descriptions of the rain cells for the mid-Atlantic region were compared to descriptions for other areas, and the similarities and differences are described. Simplified models of rain cells based on the statistical descriptions are developed for the different rain categories as a function of frequency of occurrence.

Konrad, T. G.↗

NASA NTRS1979

Radar error statistics for the space shuttle

Radar error statistics of C-band and S-band that are recommended for use with the groundtracking programs to process space shuttle tracking data are presented. The statistics are divided into two parts: bias error statistics, using the subscript B, and high frequency error statistics, using the subscript q. Bias errors may be slowly varying to constant. High frequency random errors (noise) are rapidly varying and may or may not be correlated from sample to sample. Bias errors were mainly due to hardware defects and to errors in correction for atmospheric refraction effects. High frequency noise was mainly due to hardware and due to atmospheric scintillation. Three types of atmospheric scintillation were identified: horizontal, vertical, and line of sight. This was the first time that horizontal and line of sight scintillations were identified.

Lear, W. M.↗

NASA NTRS1978

A method for determining the weak statistical stationarity of a random process

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

Sadeh, W. Z.↗

NASA NTRS1982

A two-component rain model for the prediction of attenuation statistics

A two-component rain model has been developed for calculating attenuation statistics. In contrast to most other attenuation prediction models, the two-component model calculates the occurrence probability for volume cells or debris attenuation events. The model performed significantly better than the International Radio Consultative Committee model when used for predictions on earth-satellite paths. It is expected that the model will have applications in modeling the joint statistics required for space diversity system design, the statistics of interference due to rain scatter at attenuating frequencies, and the duration statistics for attenuation events.

Crane, R. K.↗

NASA NTRS1982

Radar prediction of absolute rain fade distributions for earth-satellite paths and general methods for extrapolation of fade statistics to other locations

The first absolute rain fade distribution method described establishes absolute fade statistics at a given site by means of a sampled radar data base. The second method extrapolates absolute fade statistics from one location to another, given simultaneously measured fade and rain rate statistics at the former. Both methods employ similar conditional fade statistic concepts and long term rain rate distributions. Probability deviations in the 2-19% range, with an 11% average, were obtained upon comparison of measured and predicted levels at given attenuations. The extrapolation of fade distributions to other locations at 28 GHz showed very good agreement with measured data at three sites located in the continental temperate region.

Goldhirsh, J.↗

NASA NTRS1982

Estimation of context for statistical classification of multispectral image data

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach. This statistical classification algorithm exploits the tendency of certain ground cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context function. An unbiased estimator of the context function is discussed which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context-function estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context-function estimation techniques.

Tilton, J. C.↗

NASA NTRS1983

Statistical correlation of structural mode shapes from test measurements and NASTRAN analytical values

The software and procedures of a system of programs used to generate a report of the statistical correlation between NASTRAN modal analysis results and physical tests results from modal surveys are described. Topics discussed include: a mathematical description of statistical correlation, a user's guide for generating a statistical correlation report, a programmer's guide describing the organization and functions of individual programs leading to a statistical correlation report, and a set of examples including complete listings of programs, and input and output data.

Purves, L.↗

NASA NTRS1982

Output statistics of laser anemometers in sparsely seeded flows

It is noted that until very recently, research on this topic concentrated on the particle arrival statistics and the influence of the optical parameters on them. Little attention has been paid to the influence of subsequent processing on the measurement statistics. There is also controversy over whether the effects of the particle statistics can be measured. It is shown here that some of the confusion derives from a lack of understanding of the experimental parameters that are to be controlled or known. A rigorous framework is presented for examining the measurement statistics of such systems. To provide examples, two problems are then addressed. The first has to do with a sample and hold processor, the second with what is called a saturable processor. The sample and hold processor converts the output to a continuous signal by holding the last reading until a new one is obtained. The saturable system is one where the maximum processable rate is arrived at by the dead time of some unit in the system. At high particle rates, the processed rate is determined through the dead time.

Edwards, R. V.↗

NASA NTRS1985

Middle atmosphere general circulation statistics

With the increased availability of remote sensing data for the middle atmosphere from satellites, more analyses of the middle atmosphere circulation are being published. Some of these are process studies for limited periods, and some are statistical analyses of middle atmosphere general circulation statistics. Results from the latter class of studies will be reviewed. These include analysis of the zonally averaged middle atmosphere structure, temperature, and zonal winds; analysis of planetary wave structures, analysis of heat and momentum fluxes; and analysis of Eliassen-and-Palm flux vectors and flux divergences. Emphasis is on the annual march of these quantities; Northern and Southern Hemisphere asymmetries; and interannual variability in these statistics. Statistics involving the global ozone distribution and transports of ozone are also discussed.

Geller, M. A.↗

NASA NTRS1986

Continuum radiation from active galactic nuclei: A statistical study

The physics of the continuum spectrum of active galactic nuclei (AGNs) was examined using a large data set and rigorous statistical methods. A data base was constructed for 469 objects which include radio selected quasars, optically selected quasars, X-ray selected AGNs, BL Lac objects, and optically unidentified compact radio sources. Each object has measurements of its radio, optical, X-ray core continuum luminosity, though many of them are upper limits. Since many radio sources have extended components, the core component were carefully selected out from the total radio luminosity. With survival analysis statistical methods, which can treat upper limits correctly, these data can yield better statistical results than those previously obtained. A variety of statistical tests are performed, such as the comparison of the luminosity functions in different subsamples, and linear regressions of luminosities in different bands. Interpretation of the results leads to the following tentative conclusions: the main emission mechanism of optically selected quasars and X-ray selected AGNs is thermal, while that of BL Lac objects is synchrotron; radio selected quasars may have two different emission mechanisms in the X-ray band; BL Lac objects appear to be special cases of the radio selected quasars; some compact radio sources show the possibility of synchrotron self-Compton (SSC) in the optical band; and the spectral index between the optical and the X-ray bands depends on the optical luminosity.

Isobe, T.↗

NASA NTRS1987

Statistically determined nickel cadmium performance relationships

A statistical analysis was performed on sealed nickel cadmium cell manufacturing data and cell matching data. The cells subjected to the analysis were 30 Ah sealed Ni/Cd cells, made by General Electric. A total of 213 data parameters was investigated, including such information as plate thickness, amount of electrolyte added, weight of active material, positive and negative capacity, and charge-discharge behavior. Statistical analyses were made to determine possible correlations between test events. The data show many departures from normal distribution. Product consistency from one lot to another is an important attribute for aerospace applications. It is clear from these examples that there are some significant differences between lots. Statistical analyses are seen to be an excellent way to spot those differences. Also, it is now proven beyond doubt that battery testing is one of the leading causes of statistics.

Gross, Sidney↗

NASA NTRS1987

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay.

Manning, Robert M.↗

NASA NTRS1986

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. 1: Theoretical development and application to yearly predictions for selected cities in the United States

A rain attenuation prediction model is described for use in calculating satellite communication link availability for any specific location in the world that is characterized by an extended record of rainfall. Such a formalism is necessary for the accurate assessment of such availability predictions in the case of the small user-terminal concept of the Advanced Communication Technology Satellite (ACTS) Project. The model employs the theory of extreme value statistics to generate the necessary statistical rainrate parameters from rain data in the form compiled by the National Weather Service. These location dependent rain statistics are then applied to a rain attenuation model to obtain a yearly prediction of the occurrence of attenuation on any satellite link at that location. The predictions of this model are compared to those of the Crane Two-Component Rain Model and some empirical data and found to be very good. The model is then used to calculate rain attenuation statistics at 59 locations in the United States (including Alaska and Hawaii) for the 20 GHz downlinks and 30 GHz uplinks of the proposed ACTS system. The flexibility of this modeling formalism is such that it allows a complete and unified treatment of the temporal aspects of rain attenuation that leads to the design of an optimum stochastic power control algorithm, the purpose of which is to efficiently counter such rain fades on a satellite link.

Manning, Robert M.↗

NASA NTRS1984

General specifications for the development of a USL NASA PC R and D statistical analysis support package

The University of Southwestern Louisiana (USL) NASA PC R and D statistical analysis support package is designed to be a three-level package to allow statistical analysis for a variety of applications within the USL Data Base Management System (DBMS) contract work. The design addresses usage of the statistical facilities as a library package, as an interactive statistical analysis system, and as a batch processing package.

Dominick, Wayne D.↗

NASA NTRS1989

Chi-squared and C statistic minimization for low count per bin data

Results are presented from a computer simulation comparing two statistical fitting techniques on data samples with large and small counts per bin; the results are then related specifically to X-ray astronomy. The Marquardt and Powell minimization techniques are compared by using both to minimize the chi-squared statistic. In addition, Cash's C statistic is applied, with Powell's method, and it is shown that the C statistic produces better fits in the low-count regime than chi-squared.

Nousek, John A.↗

NASA NTRS1989

The generation of surface targets with specified surface statistics

Results are presented from efforts to generate physical surfaces from known or desired surface statistical properties, proceeding from previous work on the generation of random surfaces for use in computer simulations. The known statistical surface is extended using a bicubic spline technique; these results are interfaced with a numerically controlled machine in order to generate the physical surface. A portion of a complete surface with Gaussian statistics was constructed and tested to measure conformity to the desired statistics.

Rochier, J. D.↗

NASA NTRS1990

Attenuation statistics derived from emission measurements by a network of ground-based microwave radiometers

Two seasons of thermal emission measurements, running from December 1987 through February 1988 and from June through August 1988 of thermal emission measurements, taken by a multi-channel, ground-based microwave radiometer, are used to derive single-station zenith attenuation statistics at 20.6 and 31.65 GHz. For the summer period, statistics are also derived for 52.85 GHz. In addition, data from two dual-channel radiometers, separated from Denver by baseline distances of 49 and 168 km, are used to derive two-station attenuation diversity statistics at 20.6 and 31.65 GHz. The multi-channel radiometer is operated at Denver, Colorado; the dual-channel devices are operated at Platteville and Flagler, Colorado. The diversity statistics are presented by cumulative distributions of maximum and minimum attenuation.

Westwater, E. R.↗