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Results for “Chi-Square Distribution”

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 NTRS1981

Effect of long-term intensity variations on pulsar searches and the pulsar luminosity function

Long-term intensity data for five pulsars are used to obtain the probability density distribution of intensities for each pulsar, and it is found that they are described satisfactorily by chi-squared distributions. Based on these distributions, the number of new pulsars expected to be found on repeatedly searching the same region of the sky with the same sensitivity is given. Nearly 25 percent more new pulsars are expected to be found on the first repeat search. It is also shown that the luminosity function deduced from either a single survey or surveys with very different sensitivities is not affected by the omission of flux density variations in the calculation of selection effects. Finally, a method is proposed for deriving the luminosity function by combining the different searches of a given area on the basis of a probabilistic approach to the evaluation of selection effects.

Krishnamohan, S.↗
NASA NTRS1975

Inelastic-interaction mean free path of negative pions in tungsten

The inelastic-interaction mean free paths (lambda) of 5-, 10-, and 15-GeV/c pions have been measured by determining the distribution of first-interaction locations in a modular tungsten-scintillator ionization spectrometer. In addition to commonly used interaction signatures of a few (2-5) particles in two or three consecutive modules, a chi-squared distribution is employed to calculate the probability that the first interaction occurred at a specific depth in the spectrometer. This latter technique seems to be more reliable than use of the simpler criteria. No significant dependence of lambda on energy has been observed. In tungsten, lambda for pions is 206 (plus or minus 6) g/sq cm.

Cheshire, D. L.↗
NASA NTRS1979

Statistical analysis of multivariate atmospheric variables

Topics covered include: (1) estimation in discrete multivariate distributions; (2) a procedure to predict cloud cover frequencies in the bivariate case; (3) a program to compute conditional bivariate normal parameters; (4) the transformation of nonnormal multivariate to near-normal; (5) test of fit for the extreme value distribution based upon the generalized minimum chi-square; (6) test of fit for continuous distributions based upon the generalized minimum chi-square; (7) effect of correlated observations on confidence sets based upon chi-square statistics; and (8) generation of random variates from specified distributions.

Tubbs, J. D.↗
NASA NTRS1984

The distribution of hot spots

Statistical analyses are compared for two published hot spot data sets, one minimal set of 42 and another larger set of 117, using three different approaches. First, the earths surface is divided into 16 equal-area fractions and the observed distribution of hot spots among them is analyzed using chi-square tests. Second, cumulative distributions about the principal axes of the hot spot inertia tensor are used to describe hot spot distribution. Finally, a hot spot density function is constructed for each of the two hot spot data sets. The methods all indicate that hot spots have a nonuniform distribution, even when statistical fluctuations are considered. To the first order, hot spots are concentrated on one half of of the earth's surface area; within that portion, the distribution is consistent with a uniform distribution. The observed hot spot densities for neither data set are explained solely by plate speed.

Stefanick, M.↗
NASA NTRS1978

Comparison of high energy gamma rays from absolute value of b greater than 30 deg with the galactic neutral hydrogen distribution

High-energy gamma-ray (energy above 35 MeV) data from the SAS 2 satellite have been used to compare the intensity distribution of gamma rays with that of neutral hydrogen (H I) density along the line of sight, at high galactic latitudes (absolute values greater than 30 deg). A model has been constructed for the case where the observed gamma-ray intensity has been assumed to be the sum of a galactic component proportional to the H I distribution plus an isotropic extragalactic emission. A chi-squared test of the model parameters indicates that about 30% of the total high-latitude emission may originate within the Galaxy.

Ozel, M. E.↗
NASA NTRS1982

Updating Landsat-derived land-cover maps using change detection and masking techniques

The California Integrated Remote Sensing System's San Bernardino County Project was devised to study the utilization of a data base at a number of jurisdictional levels. The present paper discusses the implementation of change-detection and masking techniques in the updating of Landsat-derived land-cover maps. A baseline landcover classification was first created from a 1976 image, then the adjusted 1976 image was compared with a 1979 scene by the techniques of (1) multidate image classification, (2) difference image-distribution tails thresholding, (3) difference image classification, and (4) multi-dimensional chi-square analysis of a difference image. The union of the results of methods 1, 3 and 4 was used to create a mask of possible change areas between 1976 and 1979, which served to limit analysis of the update image and reduce comparison errors in unchanged areas. The techniques of spatial smoothing of change-detection products, and of combining results of difference change-detection algorithms are also shown to improve Landsat change-detection accuracies.

Likens, W.↗
NASA NTRS1987

Statistical tests for closure of plate motion circuits

Two methods, one based on a chi-square test and the second on an F-ratio test, of testing for the plate motion circuit closures are described and evaluated. The chi-square test is used to evaluate goodness of fit, and it is assumed that the assigned errors are accurate estimates of the true errors in the data. The F-ratio test is used to compare variances of distributions, and it is assumed that the relative values of assigned error are accurate. The two methods are applied to the data of Minster and Jordan (1978) on the motion of the three plates that meet at the Galapagos Triple Junction, and the motion of the three plates that meet at the Indian Ocean Triple Junction. It is noted that the F-ratio plate circuit closure test is more useful than the chi-square test for identifying systematic misfits in data because the chi-square test overestimates the errors of plate motion data.

Gordon, Richard G.↗
NASA NTRS1975

The effects of correlation on goodness of fit

Autocorrelated normal random variates were generated via computer and the effects of various levels of correlation on goodness of fit problems were studied. The results are useful in determining the distribution or estimating the parameters of populations that correlate observations such as wind speeds and temperature. The model used to generate the autocorrelated data is an autoregressive process of order 1. The Kolmogorov-Smirnov and chi-square statistics are used in the analysis. It was observed in the simulation that high positive correlations tend to shift the sample mean away from the population mean and negative correlations tend to shift the sample mean towards the population mean. In many cases, it was observed that positive and negative correlations tend to decrease the standard deviation. However, since this did not occur in all cases, no definite conclusion can be made regarding the standard deviation. Since the autoregressive process is a linear transformation, it is not surprising that normality was preserved. However, a possible extension of this problem could be to generate non-normal data and observe how the distribution is affected by correlation. Another extension might utilize another model such as autoregressive of order k or a moving average process of order k.

Kitchens, L. J.↗
NASA NTRS1987

Statistical analysis of secondary particle distributions in relativistic nucleus-nucleus collisions

The use is described of several statistical techniques to characterize structure in the angular distributions of secondary particles from nucleus-nucleus collisions in the energy range 24 to 61 GeV/nucleon. The objective of this work was to determine whether there are correlations between emitted particle intensity and angle that may be used to support the existence of the quark gluon plasma. The techniques include chi-square null hypothesis tests, the method of discrete Fourier transform analysis, and fluctuation analysis. We have also used the method of composite unit vectors to test for azimuthal asymmetry in a data set of 63 JACEE-3 events. Each method is presented in a manner that provides the reader with some practical detail regarding its application. Of those events with relatively high statistics, Fe approaches 0 at 55 GeV/nucleon was found to possess an azimuthal distribution with a highly non-random structure. No evidence of non-statistical fluctuations was found in the pseudo-rapidity distributions of the events studied. It is seen that the most effective application of these methods relies upon the availability of many events or single events that possess very high multiplicities.

Mcguire, Stephen C.↗
NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗
NASA NTRS1973

Undergraduate research report

Studies are reported of the probability distribution of yield strength for mild steel, and the application of numerical techniques to solve mechanical vibration problems. Tensile experiments were conducted for 50 cold rolled and 38 hot rolled mild steel rods. Chi-square, Kolmogro-Smirnov and goodness-of-fit methods are used to test the normality or lognormality of the experimental results. As an example of the application of numerical techniques, a nonlinear dash-pot-speing system subjected to seismic excitation is analyzed by using the fourth-order Runge-Kutta integrated method.

Yeh, H. Y.↗
NASA NTRS1975

Tables of critical values for examining compositional non-randomness in proteins and nucleic acids

A binomially distributed statistic is defined to show whether or not the proportion of a particular amino acid in a protein deviates from random expectation. An analogous statistic is derived for nucleotides in nucleic acids. These new statistics are simply related to the classical chi-squared test. They explicitly account for the compositional fluctuations imposed by the finite length of proteins, and they are more accurate than previous tables.

Laird, M.↗