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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

The asymptotic distribution of maxima in bivariate samples

The joint distribution (as n tends to infinity) of the maxima of a sample of n independent observations of a bivariate random variable (X,Y) is studied. A method is developed for deriving the asymptotic distribution of the maxima, assuming that X and Y possess asymptotic extreme-value distributions and that the probability element dF(x,y) can be expanded in a canonical series. Applied both to the bivariate normal distribution and to the bivariate gamma and compound correlated bivariate Poisson distributions, the method shows that maxima from all these distributions are asymptotically uncorrelated.

Campbell, J. W.↗
NASA NTRS1983

Some properties of a 5-parameter bivariate probability distribution

A five-parameter bivariate gamma distribution having two shape parameters, two location parameters and a correlation parameter was developed. This more general bivariate gamma distribution reduces to the known four-parameter distribution. The five-parameter distribution gives a better fit to the gust data. The statistical properties of this general bivariate gamma distribution and a hypothesis test were investigated. Although these developments have come too late in the Shuttle program to be used directly as design criteria for ascent wind gust loads, the new wind gust model has helped to explain the wind profile conditions which cause large dynamic loads. Other potential applications of the newly developed five-parameter bivariate gamma distribution are in the areas of reliability theory, signal noise, and vibration mechanics.

Tubbs, J. D.↗
NASA NTRS1992

Bivariate extreme value distributions

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Elshamy, M.↗
NASA NTRS1993

Magnetopause shape as a bivariate function of interplanetary magnetic field B(sub z) and solar wind dynamic pressure

We present a new method for determining the shape of the magnetopause as a bivariate function of the hourly averaged solar wind dynamic pressure (p) and the north-south component of the interplanetary magnetic field (IMF) B(sub z). We represent the magnetopause (for X(sub GSE) greater than -40 R(sub E)) as an ellipsoid of revolution in solar-wind-aberrated coordinates and express the (p, B(sub z)) dependence of each of the three ellipsoid parameters as a second-order (6-term) bivariate expansion in Inp and B(sub z). We define 12 overlapping bins in a normalized dimensionless (p, B(sub z)) `control space' and fit an ellipsoid to those magnetopause crossings having (p, B(sub z)) values within each bin. We also calculate the bivariate (Inp, B(sub z)) moments to second order over each bin in control space. We can then calculate the six control-space expansion coefficients for each of the three ellipsoid parameters in configuration space. From these coefficients we can derive useful diagnosis of the magnetopause shape as joint functions of p and B(sub z): the aspect ratio of the ellipsoid's minor-to-major axes; the flank distance, radius of curvature, and flaring angle (at X(sub GSE) = 0); and the subsolar distance and radius of curvature. We confirm and quantify previous results that during periods of southward B(sub z) the subsolar magnetopause moves inward, while at X(sub GSE) = 0 the flank magnetopause moves outward and the flaring angle increases.

Roelof, Edmond C.↗
NASA NTRS1982

Review of some results in bivariate density estimation

Results are reviewed for choosing smoothing parameters for some bivariate density estimators. Experience gained in comparing the effects of smoothing parameters on probability density estimators for univariate and bivariate data is summarized.

Scott, D. W.↗
NASA NTRS1990

On the level of skill in predicting maximum sunspot number - A comparative study of single variate and bivariate precursor techniques

The level of skill in predicting the size of the sunspot cycle is investigated for the two types of precursor techniques, single variate and bivariate fits, both applied to cycle 22. The present level of growth in solar activity is compared to the mean level of growth (cycles 10-21) and to the predictions based on the precursor techniques. It is shown that, for cycle 22, both single variate methods (based on geomagnetic data) and bivariate methods suggest a maximum amplitude smaller than that observed for cycle 19, and possibly for cycle 21. Compared to the mean cycle, cycle 22 is presently behaving as if it were a +2.6 sigma cycle (maximum amplitude of about 225), which means that either it will be the first cycle not to be reliably predicted by the combined precursor techniques or its deviation relative to the mean cycle will substantially decrease over the next 18 months.

Wilson, Robert M.↗
NASA NTRS1980

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Swaroop, R.↗
NASA NTRS1983

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

Campbell, C. W.↗
NASA NTRS1986

Five-Parameter Bivariate Probability Distribution

NASA technical memorandum presents four papers about five-parameter bivariate gamma class of probability distributions. With some overlap of subject matter, papers address different aspects of theories of these distributions and use in forming statistical models of such phenomena as wind gusts. Provides acceptable results for defining constraints in problems designing aircraft and spacecraft to withstand large wind-gust loads.

Tubbs, J.↗
NASA NTRS1987

Analysis of the Bivariate Parameter Wind Differences Between Jimsphere and Windsonde

An analysis is presented for the bivariate parameter differences between the FPS-16 Radar/Jimsphere and the Meteorological Sounding System (MSS) Windsonde. The Jimsphere is used as the standard to measure the ascent wind during the Space Shuttle launches at Kennedy Space Center, Florida, and the Windsonde is the backup system. In addition, a discussion of the terrestrial environment (below 20 km) and a description of the Jimsphere and Windsonde wind sensors are given. Computation of the wind statistics from 64 paired Jimsphere and Windsonde balloon releases in support of 14 Space Shuttle launches shows a good agreement between the two wind sensors. From the analysis of buildup and back-off data for various scales of distance and the comparison of the cumulative percent frequency (CPF) versus wind speed change, it is shown that the wind speed change for various scales of distances for the Jimsphere and Windsonde compare favorably.

Susko, Michael↗
NASA NTRS1993

Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Feiveson, Alan H.↗