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Results for “POISSON 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 NTRS1990

Cumulative Poisson Distribution Program

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

Bowerman, Paul N.↗
DOE OSTI2018

Fission meter and neutron detection using poisson distribution comparison

A neutron detector system and method for discriminating fissile material from non-fissile material wherein a digital data acquisition unit collects data at high rate, and in real-time processes large volumes of data directly into information that a first responder can use to discriminate materials. The system comprises counting neutrons from the unknown source and detecting excess grouped neutrons to identify fission in the unknown source. Comparison of the observed neutron count distribution with a Poisson distribution is performed to distinguish fissile material from non-fissile material.

Rowland, Mark S.↗
NASA NTRS1992

Algorithm Calculates Cumulative Poisson Distribution

Algorithm calculates accurate values of cumulative Poisson distribution under conditions where other algorithms fail because numbers are so small (underflow) or so large (overflow) that computer cannot process them. Factors inserted temporarily to prevent underflow and overflow. Implemented in CUMPOIS computer program described in "Cumulative Poisson Distribution Program" (NPO-17714).

Bowerman, Paul N.↗
NASA NTRS1999

Parameter Estimation in Astronomy with Poisson-Distributed Data: The (CHI)2(gamma) Statistic - 1

Applying the standard weighted mean formula, [Sigma (sub i)n(sub i)ssigma(sub i, sup -2)], to determine the weighted mean of data, n(sub i), drawn from a Poisson distribution, will, on average, underestimate the true mean by approx. 1 for all true mean values larger than approx.3 when the common assumption is made that the error of the i th observation is sigma(sub i) = max square root of n(sub i), 1).This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman'chi(sub 2) statistic, chi(sup 2, sub N) equivalent Sigma(sub i)((n(sub i) - y(sub i)(exp 2)) / max(n(sub i), 1), to compare Poisson - distributed data with model values, y(sub i), will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that weighted mean of data drawn from a Poisson distribution can be determined using the formula [Sigma(sub i)[n(sub i) + min(n(sub i), 1)](n(sub i) + 1)(exp -1)] / [Sigma(sub i)(n(sub i) + 1)(exp -1))], I propose that a new chi(sub 2) statistic, chi(sup 2, sub gamma) equivalent, should always be used to analyze Poisson- distributed data in preference to the modified Neyman's chi(exp 2) statistic. I demonstrated the power and usefulness of,chi(sub gamma, sup 2) minimization by using two statistical fitting techniques and five chi(exp 2) statistics to analyze simulated X-ray power - low 15 - channel spectra with large and small counts per bin. I show that chi(sub gamma, sup 2) minimization with the Levenberg - Marquardt or Powell's method can produce excellent results (mean slope errors approx. less than 3%) with spectra having as few as 25 total counts.

Mighell, Kenneth J.↗
NASA NTRS1972

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗
DOE OSTI2019

Multiple Facets of the Poisson Distribution Applicable to Health Physics Measurements

This paper discusses several ways to view the standard Poisson distribution as applied to health physics scaler counts. The intent is not so much to present calculational details but rather to present some underlying concepts. Examples are provided that illustrate the various concepts for several types of specific measurements. The concepts presented involve purely Poisson-based contributions to variance; extra-Poisson variance is presently ignored, and any counting system would be presumed to function properly and without counting loss.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1971

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

Cohen, A. C.↗
DOE OSTI2018

Neutron detection using Poisson distribution comparison independent of count rate based on correlation signals

Embodiments are directed to comparison-based methods of conditionally assessing the excess in correlation of an unknown neutron count measurement compared to the correlation present in a data defined as background, and to providing a technical definition of excess correlation intended to properly handle the measured excess correlation. The degree of correlation between an unknown source and background can be used to prevent masking of neutron count data for the source by background radiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1973

An empirical Bayes approach for the Poisson life distribution.

A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.

Canavos, G. C.↗
NASA NTRS1990

Calculation of the Poisson cumulative distribution function

A method for calculating the Poisson cdf (cumulative distribution function) is presented. The method avoids computer underflow and overflow during the process. The computer program uses this technique to calculate the Poisson cdf for arbitrary inputs. An algorithm that determines the Poisson parameter required to yield a specified value of the cdf is presented.

Bowerman, Paul N.↗
NASA NTRS2007

Managing Uncertainty Due to a Fundamental Error Source Arising from Scatterer Distribution Complexity in Radar Remote Sensing of Precipitation

The assumption that cloud and rain drops are spatially distributed according to a Poisson distribution within a scattering volume probed by a radar being used to estimate precipitation has represented bedrock theory in establishing 'rules of the game' for pulse averaging--the process needed to beat down noise to an acceptable level in the measurement of radar reflectivity factor. Based on relatively recent observations of 'realistic' spatial distributions of hydrometeor scatterers in a cloudy atmosphere motivates a renewed examination of the consequences of using a too simplified assumption underlying volume scattering--particularly in regards to the standard pulse averaging rule. Our investigation addresses two extremes, simple to complex, insofar as allowed for complexities in an underlying scatterer distribution. It is demonstrated that as the spatial distribution ranges from Poisson (a narrow distribution) to multi-fractal (much broader distribution), uncertainty in a measurement increases if the rule for pulse averaging goes unchanged from its Poisson distribution reference county. [A bounded cascade is used for the multi-fractal distribution, a regularly observed distribution vis-a-vis cloud liquid water content.] The resultant measurement uncertainty leads to a fundamental source of error in the estimation of rain rate from radar measurements, one that has been disregarded since the early 1950s when radar sets first began to be used for rainfall measuring. It is shown how this source of error can be 'managed'--under the assumption that number of data analysis experiments would be carried out, experiments involving pulse-by-pulse measurements obtained from a radar set modified to output individual pulses of reflectivity factor. For practical applications, a new parameter called normalized k-sample intensity invariance is developed to enable defining the required pulse average count according to a preferred degree of uncertainty.

Smith, Eric A.↗
NASA NTRS1984

Avalanche Photodiode Statistics in Triggered-avalanche Detection Mode

The output of a triggered avalanche mode avalanche photodiode is modeled as Poisson distributed primary avalanche events plus conditionally Poisson distributed trapped carrier induced secondary events. The moment generating function as well as the mean and variance of the diode output statistics are derived. The dispersion of the output statistics is shown to always exceed that of the Poisson distribution. Several examples are considered in detail.

Tan, H. H.↗