Search NASA⌕ Search

SEARCH · Search NASA

Results for “Normal 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Solar cell angle of incidence corrections

Literature on solar array angle of incidence corrections was found to be sparse and contained no tabular data for support. This lack along with recent data on 27 GaAs/Ge 4 cm by 4 cm cells initiated the analysis presented in this paper. The literature cites seven possible contributors to angle of incidence effects: cosine, optical front surface, edge, shadowing, UV degradation, particulate soiling, and background color. Only the first three are covered in this paper due to lack of sufficient data. The cosine correction is commonly used but is not sufficient when the incident angle is large. Fresnel reflection calculations require knowledge of the index of refraction of the coverglass front surface. The absolute index of refraction for the coverglass front surface was not known nor was it measured due to lack of funds. However, a value for the index of refraction was obtained by examining how the prediction errors varied with different assumed indices and selecting the best fit to the set of measured values. Corrections using front surface Fresnel reflection along with the cosine correction give very good predictive results when compared to measured data, except there is a definite trend away from predicted values at the larger incident angles. This trend could be related to edge effects and is illustrated by a use of a box plot of the errors and by plotting the deviation of the mean against incidence angle. The trend is for larger deviations at larger incidence angles and there may be a fourth order effect involved in the trend. A chi-squared test was used to determine if the measurement errors were normally distributed. At 10 degrees the chi-squared test failed, probably due to the very small numbers involved or a bias from the measurement procedure. All other angles showed a good fit to the normal distribution with increasing goodness-of-fit as the angles increased which reinforces the very small numbers hypothesis. The contributed data only went to 65 degrees from normal which prevented any firm conclusions about extreme angle effects although a trend in the right direction was seen. Measurement errors were estimated and found to be consistent with the conclusions that were drawn. A controlled experiment using coverglasses and cells from the same lots and extending to larger incidence angles would probably lead to further insight into the subject area.

Burger, Dale R.↗
DOE OSTI2018

Comparative Analysis of the Powers of the Two-Sample Kolmogorov–Smirnov and Anderson–Darling Tests Under Various Alternatives

In this paper we conduct a comparative analysis of the powers of the two-sample Kolmogorov–Smirnov and Anderson–Darling tests under various alternatives using simulation. We consider two examples. In the first example the alternatives to the standard normal distribution are the distributions of the so-called contaminated normal model. We study the influence of a small contamination with a positive shift on the powers of the test. In the second example the alternatives are the logistic and the Laplace distributions, which are symmetric and differ in shape from the normal distribution having a larger kurtosis coefficient and heavier tails.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

The Effect of General Statistical Fiber Misalignment on Predicted Damage Initiation in Composites

A micromechanical method is employed for the prediction of unidirectional composites in which the fiber orientation can possess various statistical misalignment distributions. The method relies on the probability-weighted averaging of the appropriate concentration tensor, which is established by the micromechanical procedure. This approach provides access to the local field quantities throughout the constituents, from which initiation of damage in the composite can be predicted. In contrast, a typical macromechanical procedure can determine the effective composite elastic properties in the presence of statistical fiber misalignment, but cannot provide the local fields. Fully random fiber distribution is presented as a special case using the proposed micromechanical method. Results are given that illustrate the effects of various amounts of fiber misalignment in terms of the standard deviations of in-plane and out-of-plane misalignment angles, where normal distributions have been employed. Damage initiation envelopes, local fields, effective moduli, and strengths are predicted for polymer and ceramic matrix composites with given normal distributions of misalignment angles, as well as fully random fiber orientation.

Micromechanical↗
NASA NTRS1974

Some qualitative remarks on the variation of the probability of error

The qualitative behavior of the probability of misclassifying observations from two normally distributed populations as the classification regions are varied in a prescribed way is described in order to provide a preliminary generalization of the results obtained by Walton for the case of normally distributed observations with varying a priori probabilities.

Walker, H. F.↗
NASA NTRS1990

Fault injection experiments using FIAT

The results of several experiments conducted using the fault-injection-based automated testing (FIAT) system are presented. FIAT is capable of emulating a variety of distributed system architectures, and it provides the capabilities to monitor system behavior and inject faults for the purpose of experimental characterization and validation of a system's dependability. The experiments consist of exhaustively injecting three separate fault types into various locations, encompassing both the code and data portions of memory images, of two distinct applications executed with several different data values and sizes. Fault types are variations of memory bit faults. The results show that there are a limited number of system-level fault manifestations. These manifestations follow a normal distribution for each fault type. Error detection latencies are found to be normally distributed. The methodology can be used to predict the system-level fault responses during the system design stage.

Barton, James H.↗
NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗
DOE OSTI2021

maranasgroup/uncFBA

In the repository are example scripts that perform uncertainty injection and propagation to flux balance analysis with outputs for a small sample size (for demonstration purpose only). For proper analysis, user should download the scripts and run for a large sample size (e.g., 10,000 samples). If you use the scripts, please cite the following Metabolic Engineering article: “Quantifying the propagation of parametric uncertainty on flux balance analysis” (https://doi.org/10.1016/j.ymben.2021.10.012) There are two subdirectories: /uncFBA/uncBiom: injection of normally distributed noise to biomass precursor coeffcients and ATP maintenance (growth-associated ATP maintenance (GAM) and non-growth associated ATP maintenance (NGAM)) /uncFBA/uncRHS: departure from steady-state by adding noise drawn from normal distribution to the RHS terms of mass balance constraints

Dinh, Hoang↗
NASA NTRS1993

The missing impact craters on Venus

The size-frequency pattern of the 842 impact craters on Venus measured to date can be well described (across four standard deviation units) as a single log normal distribution with a mean crater diameter of 14.5 km. This result was predicted in 1991 on examination of the initial Magellan analysis. If this observed distribution is close to the real distribution, the 'missing' 90 percent of the small craters and the 'anomalous' lack of surface splotches may thus be neither missing nor anomalous. I think that the missing craters and missing splotches can be satisfactorily explained by accepting that the observed distribution approximates the real one, that it is not craters that are missing but the impactors. What you see is what you got. The implication that Venus crossing impactors would have the same type of log normal distribution is consistent with recently described distribution for terrestrial craters and Earth crossing asteroids.

Speidel, D. H.↗
DOE OSTI2021

Quantitation of amiodarone and N-desethylamiodarone in single HepG2 cells by single-cell printing-liquid vortex capture-mass spectrometry

Quantitative measure of a drug and its associated metabolite(s) with single-cell resolution is often limited by sampling throughput or other compromises that limit broad use. Here, we demonstrate the use of single-cell printing-liquid vortex capture-mass spectrometry (SCP-LVC-MS) to quantitatively measure the intracellular concentrations of amiodarone (AMIO) and its metabolite, N-desethylamiodarone (NDEA), from thousands of single cells across several AMIO incubation concentrations ranging from 0 to 10 μM. Concentrations obtained by SCP-LVC-MS were validated through comparison with average assays and traditional measurement of cells in bulk. Average of SCP-LVC-MS measurements and aggregate vial collection assay the concentrations differed by < 5%. Both AMIO and NDEA had clear log-normal distributions with similar standard deviation of concentrations in the cell population. The mean of both AMIO and NDEA intracellular concentrations were positively correlated with AMIO incubation concentration, increasing from 0.026 to 0.520 and 0.0055 to 0.048 mM for AMIO and NDEA, respectively. The standard deviation of AMIO and NDEA log-normal distribution fits were relatively similar in value across incubation concentrations, 0.15–0.19 log 10 (mM), and exhibited a linear trend with respect to each other. The single cell-resolved conversion ratio of AMIO to NDEA increased with decreasing incubation concentration, 7 ± 2%, 18 ± 3%, and 20 ± 7% for 10.0, 1.0, and 0.1 μM AMIO incubation concentrations, respectively. Finally, association with simultaneously measured lipids had several ions with statistically significant difference in intensity but no clear correlations with AMIO intracellular content was observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Slant path L- and S-Band tree shadowing measurements

This contribution presents selected results from simultaneous L- and S-Band slant-path fade measurements through a pecan, a cottonwood, and a pine tree employing a tower-mounted transmitter and dual-frequency receiver. A single, circularly-polarized antenna was used at each end of the link. The objective was to provide information for personal communications satellite design on the correlation of tree shadowing between frequencies near 1620 and 2500 MHz. Fades were measured along 10 m lateral distance with 5 cm spacing. Instantaneous fade differences between L- and S-Band exhibited normal distribution with means usually near 0 dB and standard deviations from 5.2 to 7.5 dB. The cottonwood tree was an exception, with 5.4 dB higher average fading at S- than at L-Band. The spatial autocorrelation reduced to near zero with lags of about 10 lambda. The fade slope in dB/MHz is normally distributed with zero mean and standard deviation increasing with fade level.

Vogel, Wolfhard J.↗
NASA NTRS2011

Fermi/GBM Observations of SGRJ0501 + 4516 Bursts

We present our temporal and spectral analyses of 29 bursts from SGRJ0501+4516, detected with the Gamma-ray Burst Monitor onboard the Fermi Gamma-ray Space Telescope during the 13 days of the source activation in 2008 (August 22 to September 3). We find that the T(sub 90) durations of the bursts can be fit with a log-normal distribution with a mean value of approx. 123 ms. We also estimate for the first time event durations of Soft Gamma Repeater (SGR) bursts in photon space (i.e., using their deconvolved spectra) and find that these are very similar to the T(sub 90)s estimated in count space (following a log-normal distribution with a mean value of approx. 124 ms). We fit the time-integrated spectra for each burst and the time-resolved spectra of the five brightest bursts with several models. We find that a single power law with an exponential cutoff model fits all 29 bursts well, while 18 of the events can also be fit with two black body functions. We expand on the physical interpretation of these two models and we compare their parameters and discuss their evolution. We show that the time-integrated and time-resolved spectra reveal that E(sub peak) decreases with energy flux (and fluence) to a minimum of approx. 30 keV at F = 8.7 x 10(exp -6)erg/sq cm/s, increasing steadily afterwards. Two more sources exhibit a similar trend: SGRs J1550 - 5418 and 1806 - 20. The isotropic luminosity, L(sub iso), corresponding to these flux values is roughly similar for all sources (0.4 - l.5 x 10(exp 40) erg/s.

Lin, Lin↗
NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗
NASA NTRS2003

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Howell, L. W., Jr.↗
NASA NTRS1988

Solution of an integral equation encountered in studies on radiative transfer in completely absorbing leaf canopies

The leaf normal distribution function is related to the extinction coefficient of direct solar radiation by a Fredholm integral equation of the first kind. The integral equation is solved by the method of constrained least squares. The solutions are stable and correct only in extreme cases and, in general, it is not possible to recover an arbitrary leaf normal distribution function.

Myneni, Ranga B.↗
DOE OSTI2017

The Nickel Mass Distribution of Normal Type II Supernovae

Core-collapse supernova (SN) explosions expose the structure and environment of massive stars at the moment of their death. We use the global fitting technique of Pejcha and Prieto to estimate a set of physical parameters of 19 normal SNe II, such as their distance moduli, reddenings, {sup 56}Ni masses M{sub Ni}, and explosion energies E{sub exp} from multicolor light curves and photospheric velocity curves. We confirm and characterize known correlations between M{sub Ni} and bolometric luminosity at 50 days after the explosion, and between M{sub Ni} and E{sub exp}. We pay special attention to the observed distribution of M{sub Ni} coming from a joint sample of 38 SNe II, which can be described as a skewed-Gaussian-like distribution between 0.005 M{sub ⊙} and 0.280 M{sub ⊙}, with a median of 0.031 M{sub ⊙}, mean of 0.046 M{sub ⊙}, standard deviation of 0.048 M{sub ⊙}, and skewness of 3.050. We use a two-sample Kolmogorov–Smirnov test and two-sample Anderson–Darling test to compare the observed distribution of M{sub Ni} to results from theoretical hydrodynamical codes of core-collapse explosions with the neutrino mechanism presented in the literature. Our results show that the theoretical distributions obtained from the codes tested in this work, KEPLER and Prometheus Hot Bubble, are compatible with the observations irrespective of different pre-SN calibrations and different maximum mass of the progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Testing Nesting DXTRAN Spheres for Neutron Transport in Air

The deterministic transport sphere (DXTRAN sphere) is a technology that can be utilized in MCNP for improving sampling in the vicinity of a particular geometry, when the solid angle, between the source and particular geometry, is small. At a collision event, a DXTRAN particle is created and deterministically transported to the DXTRAN sphere, while the colliding particle (NONDXTRAN particle) continues transporting as if no DXTRAN event had occurred. Weight is balanced by killing the NONDXTRAN particle when traversing the DXTRAN sphere. If set up correctly, the DXTRAN particle placed on the DXTRAN sphere has a high probability of interacting with the geometry within the DXTRAN sphere. The Central Limit Theorem (CLT) states that the estimated mean approaches a normal distribution with known variance as the number of random samples grows sufficiently large. In reality the variance is seldom known and therefore must be estimated. In a Monte Carlo calculation, one must determine when the number of random samples is sufficiently large for the CLT to be satisfied. For the CLT to be satisfied, the first two moments (mean and variance) must exist. The second moment, the variance of a normal distribution is estimated. The slope test, which uses the largest 201 history scores of each tally fluctuation chart (TFC) bin fit to a Pareto function, is used to determine if the largest history scores decrease faster than 1/x{sup 3}. If the slope is less than 3, then enough histories have not yet been sampled such to meet the second moment existence requirement of the CLT. Usually, a slope of less than 3 indicates that the effects of high weight scores have not been satisfactorily sampled; such a consequence can also be manifested in examining trends in the 4. moment, the variance of the variance (VOV). For example, when examining the TFC, if the VOV is monotonically decreasing for a few sets of histories and then drastically increases for the next set of histories, chances are a rare high weight score, significantly greater than the average score, was encountered. As a result of the 1/R{sup 2} term, a point detector can achieve an extremely high weight, much greater than the average, as the distance from collision to point detector approaches zero. To remedy this difficulty, a 'radius of exclusion' is applied, where within the radius of exclusion 'the point detector estimate is assumed to be the average flux uniformly distributed'. A DXTRAN sphere can suffer from the same weight fluctuation as collisions in the vicinity of the DXTRAN sphere produce much larger weights than collisions happening far from the DXTRAN sphere. If the rare large weight put on the DXTRAN sphere then scores in a tally, there will be a significant increase in the VOV and the slope may drop below 3. To compliment that analysis, here we utilize an air composition and density that varies as a function of altitude, detailing the trials and tribulations of attempting to pass the 10 statistical checks for a variety of single and nested DXTRAN sphere approaches. The objective here is to illuminate important considerations for radiation transport problems with small solid angles in a scatter medium of few mean free paths (MFPs)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Formulation of autoconversion and drop spectra shape in shallow cumulus clouds

Two-moment autoconversion parameterizations as compared to accretion parameterizations exhibit significant errors suggesting that additional moments are needed to increase their accuracy. We develop a three-moment autoconversion parameterization using output from an LES model with size-resolved microphysics. Adding the third moment decreases the errors of parameterization and improves precipitation prediction. However, the errors are still significantly larger than errors of accretion rate. An analysis of the cloud drop size distributions (DSDs) in the simulated tropical convective cloud system reveals that most of DSDs have a significant fraction of cloud liquid water content (qc) in the mid-size droplet range (radii from 20 to 40 microns). Our data indicates that more than 30% of DSDs have over half of qc contained in the mid-size range and about 60% of spectra have, at least, one third of qc in this range. Even when the rain/drizzle mode is small (radar reflectivity Z < -10 dBZ), there is a significant number of spectra in which fraction of qc in the mid-size range is as large as 60%. These DSDs are more complex than the frequently used single-mode Gamma or Log-normal distributions, which usually do not have a considerable tail extending to the mid-size range and can be defined by three microphysical moments. The need to define DSDs by more than three moments explains the large errors in the three-moment autoconversion parameterization. The limitation of three-parameter Gamma or Log-normal distributions should be kept in mind when applying them in precipitating shallow Cu clouds.

Kogan, Yefim↗
NASA NTRS1989

On the statistics of El Nino occurrences and the relationship of El Nino to volcanic and solar/geomagnetic activity

El Nino is conventionally defined as an anomalous and persistent warming of the waters off the coasts of Ecuador and Peru in the eastern equatorial Pacific, having onset usually in Southern Hemispheric summer/fall. Some of the statistical aspects of El Nino occurrences are examined, especially as they relate to the normal distribution and to possible associations with volcanic, solar, and geomagnetic activity. With regard to the very strong El Nino of 1982 to 1983, it is noted that, although it may very well be related to the 1982 eruptions of El Chichon, the event occurred essentially on time (with respect to the past behavior of elapsed times between successive El Nino events; a moderate-to-stronger El Nino was expected during the interval 1978 to 1982, assuming that El Nino occurrences are normally distributed, having a mean elapsed time between successive onsets of 4 years and a standard deviation of 2 years and a last known occurrence in 1976). Also, although not widely recognized, the whole of 1982 was a record year for geomagnetic activity (based on the aa geomagnetic index, with the aa index registering an all time high in February 1982), perhaps, important for determining a possible trigger for this and other El Nino events. A major feature is an extensive bibliography (325 entries) on El Nino and volcanic-solar-geomagnetic effects on climate. Also, included is a tabular listing of the 94 major volcanic eruptions of 1835 to 1986.

Wilson, Robert M.↗