Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exponential 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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Statistical Modeling of Landscape Pattern and the Effects of Coarse Spatial Resolution

Analysis of classified satellite imagery was conducted to characterize errors in estimates of area based on coarse resolution satellite imagery which are due to distortions in sizes of small fragments, and to explore the feasibility of correcting for these errors using a statistical modeling approach. Sizes of bodies of open water on European Remote-Sensing (ERS-1) synthetic aperture radar (SAR) and fire scars on Landsat Multispectral Scanner (MSS) imagery were measured using geographic information system (GIS) software. Statistical analysis of the smaller scars and ponds as observed with this imagery of relatively fine resolution demonstrated that the distribution of the sizes could be modeled by either of two types of statistical distributions-a power distribution related to fractal processes or a simple exponential distribution. A comparison of the size distribution of small burn scars as observed with Landsat with the distribution observed with the much coarser Advanced Very High Resolution Radiometer (AVHRR) imagery revealed effects of coarse resolution, each of which were associated with a particular size range, and whose net effect accounted for the bias in total burn area due to coarse spatial resolution. Size dependent area correction procedures are therefore feasible. A statistical modeling approach to area estimation, based models of the underlying and observed size distributions of fragments in the scene, may lead to a procedure which requires little or no ancillary data.

Hlavka, C. A.↗
NASA NTRS1988

The hydrogen density of the local interstellar medium and an upper limit to the galactic glow determined from Pioneer 10 ultraviolet photometer observations

Pioneer 10 Lyman-alpha data obtained beyond the heliocentric distance of 30 AU are used here to determine the local ISM hydrogen density and downwind Galactic glow. The resulting asymptotic interstellar hydrogen density obtained using a conventional interplanetary model is 0.06/cu cm, and the Galactic Lyman-alpha glow is found to be negligible in the downwind direction. Discrepancies are found between observations and the conventional theoretical predictions of the glow dependence on radial distance. Based solely on data obtained between 30 and 39 AU, a better fit is obtained with a constant density distribution beyond 30 AU. In this case, a density of 0.05/cu cm and Galactic glow of 1.5 R is obtained. These results suggest that a complex density distribution may be more appropriate than either the conventional exponential distribution or the constant distribution.

Wu, F. M.↗
NASA NTRS1995

Arctic sea ice leads from advanced very high resolution radiometer images

A large number of advanced very high resolution radiometer (AVHRR) images from throughout 1989 are analyzed to determine lead characteristics. The units of analysis are square 200-km cells, and there are 270 such cells in the data set. Clouds are masked manually. Leads determine from images of the potential open water delta, a scaled version of the surface temperature or albedo that weights thin ice by its thermal or brightness impact. The lead fraction is determined as the mean delta, the monthly mean lead fraction ranges from 0.02 in winter to 0.06 in summer in the central Arctic and is near 0.08 in the winter in the peripheral seas. A method of accounting for lead width sampling errors due to the finite sample areas is introduced. In the central Arctic the observed mean lead width for a threshold of delta = 0.1 ranges from 2 or 3 km (near the resolution of the instrument) in the winter to 6 km in the summer. In the peripheral seas it is about 5 km in the winter. Width distributions are often more heavily weighted in the tail than exponential distributions and are well approximated by a power law. The along-track, number density power law N = aw(exp -6) has a mean exponent of b = 1.60 (standard deviation 0.18) and shows some seasonal variability. Mean floe widths in the central Arctic are 40 to 50 km in the winter, dropping to about 10 km in the summer. For floes the power law has a mean exponent of 0.93 and exhibits a clearer annual cycle. Lead orientation is determined with a method based on the direction of maximum extent.

Lindsay, R. W.↗
NASA NTRS1991

Statistical structural analysis of rotor impact ice shedding

The statistical characteristics of impact ice shear strength are analyzed, with emphasis placed on the most probable shear strength and statistical distribution of an ice deposit. Several distribution types are considered: the Weibull, two-parameter Weibull, and exponential distributions, as well as the Gumbell distribution of the smallest extreme and the Gumbell distribution of the largest extreme. It is concluded that the Weibull distribution yields the best results; however, the expected life, shape parameter, and scale parameter should be determined separately for each case of varying wind speed and droplet size. The theoretical predictions of shear stresses in a specific rotating ice shape are compared, and it is noted that when the effects of lift are added to the theoretical model and the interference is calculated with a new mean and standard deviation, the probability of ice shed is computed as 36.64 pct.

Kellacky, C. J.↗
NASA NTRS1995

HF radar signatures of the cusp and low-latitude boundary layer

Continuous ground-based observations of ionospheric and magnetospheric regions are critical to the Geospace Environmental Modeling (GEM) program. It is therefore important to establish clear intercalibrations between different ground-based instruments and satellites in order to clearly place the ground-based observations in context with the corresponding in situ satellite measurements. HF-radars operating at high latitudes are capable of observing very large spatial regions of the ionosphere on a nearly continuous basis. In this paper we report on an intercalibration study made using the Polar Anglo-American Conjugate Radar Experiment radars located at Goose Bay, Labrador, and Halley Station, Antarctica, and the Defense Meteorological Satellite Program (DMSP) satellites. The DMSP satellite data are used to provide clear identifications of the ionospheric cusp and the low-latitude boundary layer (LLBL). The radar data for eight cusp events and eight LLBL events have been examined in order to determine a radar signature of these ionospheric regions. This intercalibraion indicates that the cusp is always characterized by wide, complex Doppler power spectra, whereas the LLBL is usually found to have spectra dominated by a single component. The distribution of spectral widths in the cusp is of a generally Gaussian form with a peak at about 220 m/s. The distribution of spectral widths in the LLBL is more like an exponential distribution, with the peak of the distribution occurring at about 50 m/s. There are a few cases in the LLBL where the Doppler power spectra are strikingly similar to those observed in the cusp.

Baker, K. B.↗
NASA NTRS1978

The relative abundances of the elements silicon through nickel in the low energy galactic cosmic rays

Measurements of the relative abundances of the elements Si through Ni in galactic cosmic rays in the energy interval 72 to 450 MeV/nucleon are reported based on data collected by a cosmic-ray telescope on the IMP 8 satellite. The measured abundances are compared with propagation calculations using various distributions of path lengths. It is found that the measurements favor an exponential distribution of path lengths truncated at short path lengths. The source abundances of Si, Ca, Fe, and Ni derived by extrapolating the measured abundances back to the source are shown to be comparable to the solar-system abundances. The relevance of the measurements of Sc through Mn to the Mn-54 radioactive decay is examined.

Garcia-Munoz, M.↗
NASA NTRS2007

On the Determination of Poisson Statistics for Haystack Radar Observations of Orbital Debris

A convenient and powerful method is used to determine if radar detections of orbital debris are observed according to Poisson statistics. This is done by analyzing the time interval between detection events. For Poisson statistics, the probability distribution of the time interval between events is shown to be an exponential distribution. This distribution is a special case of the Erlang distribution that is used in estimating traffic loads on telecommunication networks. Poisson statistics form the basis of many orbital debris models but the statistical basis of these models has not been clearly demonstrated empirically until now. Interestingly, during the fiscal year 2003 observations with the Haystack radar in a fixed staring mode, there are no statistically significant deviations observed from that expected with Poisson statistics, either independent or dependent of altitude or inclination. One would potentially expect some significant clustering of events in time as a result of satellite breakups, but the presence of Poisson statistics indicates that such debris disperse rapidly with respect to Haystack's very narrow radar beam. An exception to Poisson statistics is observed in the months following the intentional breakup of the Fengyun satellite in January 2007.

Stokely, Christopher L.↗
NASA NTRS1972

Dynamics of stratified liquids in the presence of space charge.

The dispersion characteristics of small signal electrohydrodynamic space charge and polarization waves in continuously and discretely stratified liquids are developed. The liquids, modeled as incompressible, inviscid, and perfectly insulating have distributions of mass density, charge density, permittivity, and electric field. A general set of relations for perturbation field and flow variables defined for a prototype layer are used to describe the dynamics of many superposed planar layers. It is shown that the general relations can be used to represent systems of coupled layers which approximate continuous distributions by a series of step functions. Specific examples of weak gradient and exponential distributions are presented showing that the solution found directly from the distributed theory is approached by the system of coupled layers, if the limit is taken in which the number of layers become large while each layer thickness approaches zero.

Zahn, M.↗
NASA NTRS1986

At least some errors are randomly generated (Freud was wrong)

An experiment was carried out to expose something about human error generating mechanisms. In the context of the experiment, an error was made when a subject pressed the wrong key on a computer keyboard or pressed no key at all in the time allotted. These might be considered, respectively, errors of substitution and errors of omission. Each of seven subjects saw a sequence of three digital numbers, made an easily learned binary judgement about each, and was to press the appropriate one of two keys. Each session consisted of 1,000 presentations of randomly permuted, fixed numbers broken into 10 blocks of 100. One of two keys should have been pressed within one second of the onset of each stimulus. These data were subjected to statistical analyses in order to probe the nature of the error generating mechanisms. Goodness of fit tests for a Poisson distribution for the number of errors per 50 trial interval and for an exponential distribution of the length of the intervals between errors were carried out. There is evidence for an endogenous mechanism that may best be described as a random error generator. Furthermore, an item analysis of the number of errors produced per stimulus suggests the existence of a second mechanism operating on task driven factors producing exogenous errors. Some errors, at least, are the result of constant probability generating mechanisms with error rate idiosyncratically determined for each subject.

Sellen, A. J.↗
NASA NTRS1984

Software reliability: Additional investigations into modeling with replicated experiments

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Nagel, P. M.↗
NASA NTRS1986

Spatial modelling of total storm rainfall

The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.

Rodriguez-Iturbe, I.↗
NASA NTRS2011

Distribution Functions of Sizes and Fluxes Determined from Supra-Arcade Downflows

The frequency distributions of sizes and fluxes of supra-arcade downflows (SADs) provide information about the process of their creation. For example, a fractal creation process may be expected to yield a power-law distribution of sizes and/or fluxes. We examine 120 cross-sectional areas and magnetic flux estimates found by Savage & McKenzie for SADs, and find that (1) the areas are consistent with a log-normal distribution and (2) the fluxes are consistent with both a log-normal and an exponential distribution. Neither set of measurements is compatible with a power-law distribution nor a normal distribution. As a demonstration of the applicability of these findings to improved understanding of reconnection, we consider a simple SAD growth scenario with minimal assumptions, capable of producing a log-normal distribution.

McKenzie, D.↗
NASA NTRS2019

On the Maximum Expected Electric Field in Electrically Small, Undermoded Enclosures

This paper reports the experimental validation of an improved statistical model for the prediction of maximum expected electric field in electrically small and under-moded enclosures. The aerospace community is interested in application of Hill's statistical models to design of avionics boxes for shielding effectiveness and for tailoring EMC test requirements for critical applications. However, it is observed that the probability distribution for mean-squared electric field in an electrically small enclosure differs from the exponential distribution which is widely used in reverberation chamber testing. It is postulated here that the difference is attributable to the under-moded character of the small enclosure.

Bremner, Paul↗
NASA NTRS1985

Exponential order statistic models of software reliability growth

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Miller, D. R.↗
NASA NTRS1986

Exponential order statistic models of software reliability growth

Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Miller, D. R.↗
NASA NTRS2019

On the Maximum Expected Electric Field in Electrically Small, Undermoded Enclosures

This paper reports the experimental validation of an improved statistical model for the prediction of maximum expected electric field in electrically small and under-moded enclosures. The aerospace community is interested in application of Hill’s statistical models to design of avionics boxes for shielding effectiveness and for tailoring EMC test requirements for critical applications. However, it is observed that the probability distribution for mean-squared electric field (|E(sub x)|(exp 2)) in an electrically small enclosure differs from the exponential distribution which is widely used in reverberation chamber testing. It is postulated here that the difference is attributable to the under-moded character of the small enclosure. We will define “under-moded” as the condition where a single excitation frequency does not excite enough closely spaced resonant modes to achieve Hill’s assumption of an isotropic (or fully diffuse) plane wave field in the enclosure.

Bremner, P. G.↗
NASA NTRS1985

Light scattering in a spherical, exponential atmosphere, with applications to Venus

In the present discussion of the problem presented by the reflection of light from an optically thick spherical atmosphere, in which the scatterers are distributed exponentially with a scale height that is small by comparison to the radius of the planet, exact formal solutions are obtained for the single scattered component. The results obtained are applied to the analysis of the Mariner 10 limb and terminator images of Venus, which show a detached haze layer as a planetwide feature that is similar in location, scale height, and thickness during both Pioneer Venus and Mariner 10 missions, by contrast to the dramatically altered lower haze. The possible nature of the limb hazes is discussed.

Wallach, D.↗