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Correlations between X-ray and type 3 radio emission of solar bursts are described through a bivariate distribution function. Procedures for determining the form of this distribution are described. A model is constructed to explain the correlation between the X-ray spectral index and the ratio of X-ray to radio intensities. Implications of the model are discussed.
Algorithm generates pairs drawn from bivariate normal distribution with any desired values of two means, two standard deviations, and correlation coefficient.
Given N distinct points (X sub i, Y sub i) and N real numbers Z sub i, BSPLASH constructs a function G (x, y) that satisfies G (x sub i, y sub i) = Z sub i for i = 1,..., N. This C(2) interpolant consists of a bicubic spline approximation and Shepard's bivariate interpolant.
A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the parameters to be estimated are density functions. Density estimators can be non-parametric (computed independently of model identified) or parametric-select (approximated by finite parametric models that can provide standard models whose fit can be tested). Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. Applications of these ideas are outlined to the problems of modeling: (1) univariate data; (2) bivariate data and tests for independence; and (3) two samples and likelihood ratios. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models.
General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.
The remote sensing of rain amounts is of great interest for a great variety of operational applications, including hydrology, hydroelectricity and agriculture is discussed. The microwave radiometer represents the most obvious technique, however, poor spatial and temporal resolution, together with the problems associated with the estimation of effective rain layer height make visible and IR techniques more promising at the present time. Based on bivariate frequency distribution of brightness versus temperature, brightness enhancing or infrared technique alone may be inadequate to deduce details of convective activity. It is implied that better estimates of rainfall will come from visible and IR observations combined than from either used alone. The technique identifies clouds with high probability of rain as those which have large optical and presumably physical thickness as measured by the visible albedo in comparison with their height, determined by the intensity of the IR emission.
The methods proposed by Smith and Adelfang (1981) and Smith et al. (1982) are used to calculate probabilities over rectangles and sectors of the gust magnitude-gust length plane; probabilities over the same regions are also calculated from the observed distributions and a comparison is also presented to demonstrate the accuracy of the statistical model. These and other statistical results are calculated from samples of Jimsphere wind profiles at Cape Canaveral. The results are presented for a variety of wavelength bands, altitudes, and seasons. It is shown that wind perturbations observed in Jimsphere wind profiles in various wavelength bands can be analyzed by using digital filters. The relationship between gust magnitude and gust length is modeled with the bivariate gamma distribution. It is pointed out that application of the model to calculate probabilities over specific areas of the gust magnitude-gust length plane can be useful in aerospace design.
Correlations between X-ray and type 3 radio emission of solar bursts are described through a bivariate distribution function. Procedures for determining the form of this distribution are described. A model is constructed to explain the correlation between the X-ray spectral index and the ratio of X-ray to radio intensities. Implications of the model are discussed. Previously announced in STAR as N82-32243
Wind gust data were analyzed by statistical and mathematical procedures, developed for the bivariate gamma distribution. The results of the analysis are summarized.
The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.
This paper describes the development of a hybrid computer simulation of a TF34-GE-100 turbofan engine with post-stall capability. The simulation operates in real-time and will be used to test and evaluate stall recovery control modes for this engine. The simulation calculations are performed by an analog computer with a peripheral multivariable function generation unit used for computing bivariate functions. Tabular listings of a simulation variables are obtained by interfacing to a digital computer and using a custom software package for data collection and display.
For the period considered, December 1977 through February 1978, bivariate Gaussian discriminant function cloud identification revealed that more than 93 percent of the 8-km resolution GOES infrared pixels were cloud contaminated. Cloud-free in-situ calibration points were distributed in nonrandom groups; this resulted in systematic errors when using least squares techniques. Surfaces and regression lines were least squares fitted between satellite and in-situ data; use was also made of differences and ratios. The best results were achieved with a regression in the form of the infrared radiative transfer equation; but this was no better than + or - 0.9 K. Because of extensive cloudiness, the linear regressions were seldom useful, and temperature ratios with + or - 1.3 K experimental errors best represent the applicability of GEOS data to sea surface temperatures.
The relationship between the ocean's normalized radar cross section (NRCS) at 14.6 GHz and the surface wind vector is derived using the 3 months of Seasat microwave scatterometer (SASS) measurements. The derivation is based on the statistics of the SASS observations, and no in situ measurements are required, other than a mean global wind speed, which comes from climatology. The frequency distribution of the global wind vectors observed by SASS is assumed to be a bivariate normal probability function. A NRCS model function is found that maps the assumed wind vector statistics into the observed SASS NRCS statistics. This function is compared with a NRCS model coming from the Joint Air Sea Interaction Experiment (JASIN) and with aircraft scatterometer measurements. The results indicate that the statistically derived NRCS model is an improvement over the JASIN model, which was based on a limited number of in situ anemometer measurements.
The recent discovery of small active nuclei (via emission lines) in normal spiral galaxies greatly expands the range of the quasar phenomenon. By using the relationship between Lx and L(H-alpha) found in more luminous Seyfert galaxies and assuming that it holds for smaller active nuclei, a bivariate X-ray luminosity function can be calculated. This luminosity function fits naturally onto the higher luminosity X-ray luminosity function derived from the HEAO-1/A2 survey. The contribution to the X-ray background from small active nuclei hiding in large spiral galaxies is greater than 15 percent.
This paper describes the development of a hybrid computer simulation of a TF34-GE-100 turbofan engine with post-stall capability. The simulation operates in real-time and will be used to test and evaluate stall recovery control modes for this engine. The simulation calculations are performed by an analog computer with a peripheral multivariable function generation unit used for computing bivariate functions. Tabular listings of simulation variables are obtained by interfacing to a digital computer and using a custom software package for data collection and display.
Link margin estimates are calculated for 30/20 GHz satellite communication systems employing closely-spaced (4 to 100 km) 'dual diversity' switched ground sites. The link margin estimates are based on a new analysis in which the bivariate rain attenuation density function for two correlated ground sites is modelled by an exponential density function. The results of the exponential density function analysis enable derivation of a direct relation between rain margin estimates and probability of exceedance (link availability). Margins typically in the range 2 to 12 dB are calculated for various ground site separations and summarized for seven city locations and five satellite orbit positions over the U.S. The results can be easily extended to other EHF satellite frequencies and other locations.
Several computer subroutines have been developed that interpolate three types of nonanalytic functions: univariate, bivariate, and map. The routines use data in floating-point form. However, because they are written for use on a 16-bit Intel 8086 system with an 8087 mathematical coprocessor, they execute as fast as routines using data in scaled integer form. Although all of the routines are written in assembly language, they have been implemented in a modular fashion so as to facilitate their use with high-level languages.
The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.