scholarly journals The Effect of Estimating the Shape Parameter on Probability Distributions Using the Moment Method

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Hamza Ibrahim Hamza
Keyword(s):  
Shape Parameter ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Matlab Program ◽  
Best Estimate ◽  
The Mean ◽  
The Moment

  The purpose of this paper was to identify the values ​​of the parameters of the shape of the binomial, Poisson and natural distributions. Using the estimation method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values ​​of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions, Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions. For estimating the parameter of figure (0.5), (0.7), (0.9) Among distributions. The paper also issued a number of recommendations, most notably the use of binomial distribution to estimate the parameter of the figure (0.9) at the size of sample (10), (30), (50), (70).  

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

Best-Estimate Plus Uncertainty Analysis of CANDU Fuel Reliability Using Manufacturing and Simulated Core Data

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Jason J. Song ◽  
Paul K. Chan ◽  
Hugues W. Bonin ◽  
Mahesh Pandey
Keyword(s):  
Internal Pressure ◽  
Probability Distributions ◽  
Real Data ◽  
Simulation Method ◽  
Failure Criteria ◽  
Hoop Strain ◽  
Fuel Performance ◽  
Best Estimate ◽  
Average Improvement ◽  
Centerline Temperature

Abstract A novel method of assessing the reliability of 37-element Canada deuterium uranium (reactor) (CANDU) fuel bundle was explored. The method implements a “best-estimate plus uncertainty” (BEPU) approach where a probabilistic treatment of manufacturing and operating inputs is used to predict fuel performance. The fuel performance was predicted using the Canadian industry standard codes for fuel performance, ELESTRESS and ELOCA, which, respectively, model fuel behaviors during normal and transient conditions. The outputs of the codes were compared against failure criteria from industry norms to determine the probability of failure. A Monte Carlo simulation method was applied to analyze this problem. Probability distributions of manufacturing input variables were estimated from real data, which were then randomly sampled. The inputs for fuel burnup and power were simulated using core-following data generated using a three-dimensional diffusion code, the Reactor Fuelling Simulation Program (RFSP), which were also then randomly sampled. The results of the simulations predict significant improvements in margins to limits for all performance parameters. An average improvement of 500 °C in centerline temperature, 10 °C in sheath temperature, 12 MPa in element internal pressure, and 0.8% in pellet end sheath hoop strain was predicted for the highest-powered region of the core, during normal operations, in comparison with the limit-of-envelope (LOE) benchmark. An 80% reactor overhead break (ROH) transient simulation was also simulated, and an average improvement of 500 °C in centerline temperature, 150 °C in sheath temperature, 6.5 MPa in internal pressure, and 2% in sheath hoop strain was predicted.

scholarly journals Simulating more accurate snow maps for Norway with MCMC parameter estimation method

2014 ◽  
Vol 8 (2) ◽  
pp. 1973-2003 ◽  
Author(s):  
T. M. Saloranta
Keyword(s):  
Snow Water Equivalent ◽  
Probability Distributions ◽  
Estimation Method ◽  
Model Performance ◽  
Simulation Method ◽  
Future Research ◽  
Model Parameters ◽  
Data Set ◽  
Mcmc Simulation ◽  
Snow Model

Abstract. The seNorge snow model produces daily updated maps (1 km × 1 km resolution) of snow conditions for Norway which are used by the national flood, avalanche and landslide forecasting services, among others. The snow model uses gridded observations of daily temperature and precipitation as its input forcing. In this paper the revisions made to the new seNorge snow model code (v.1.1.1) are described, and a systematic model analysis is performed by first revealing the most influential key parameters by the Extended FAST sensitivity analysis and then estimating their probability distributions by the MCMC simulation method, using 565 observations of snow water equivalent (SWE) and snow density (ρ). The MCMC simulation resulted in rather narrow posterior distributions for the four estimated model parameters, and enhanced the model performance and snow map quality significantly, mainly by removing the known significant overestimation biases in SWE and ρ. In the new model version (v.1.1.1) the Nash–Sutcliffe (NS) model performance values are now well positive (NS = 0.61 for SWE and NS = 0.30 for ρ), in contrast to the much lower negative NS-values of the previous model (v.1.1). Moreover, the model evaluation against approximately 400 000 point measurements of snow depth shows improvement in the simulated percentage of "good match"-stations (76–84% before April, and still 65% at the end of April). Future research efforts should focus on decreasing the variability in the model fit with observations (i.e. model precision) by further improvements in the seNorge snow model and its important fundament, the gridded meteorological input data set used as its forcing.

scholarly journals A Neural Network Approach to Weibull Distributed Sea Clutter Parameter's Estimation

2015 ◽  
Vol 18 (56) ◽  
pp. 3 ◽  
Author(s):  
José Raúl Machado Fernández ◽  
Jesus de la Concepción Bacallao Vidal ◽  
Nelso Chávez Ferry
Keyword(s):  
Shape Parameter ◽  
Probability Distributions ◽  
A Priori ◽  
Operating Conditions ◽  
Sea Surface ◽  
Network Approach ◽  
Sea Clutter ◽  
Target Information ◽  
Neural Network Approach ◽  
The Mean

The main problem faced by sea radars is the elimination of an undesirable signal that appears mixed with target information: sea clutter. The clutter results from the echo caused by the rebound of the primary emission at sea surface. One of the most popular probability distributions in clutter modelling is the Weibull distribution. Helpful in efficient detectors’ design, a system able to recognize the Weibull shape parameter knowing a priori that the mean of the distribution is equal to zero is proposed. The result is appropriate for real time operating conditions as it is based on a neural networks approximation in the estimator role.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals An Estimation Method of Continuous Non-Invasive Arterial Blood Pressure Waveform Using Photoplethysmography: A U-Net Architecture-Based Approach

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1867
Author(s):  
Tasbiraha Athaya ◽  
Sunwoong Choi
Keyword(s):  
Blood Pressure ◽  
Cardiovascular Health ◽  
Estimation Method ◽  
Absolute Error ◽  
British Hypertension Society ◽  
Non Invasive ◽  
Arterial Blood ◽  
Blood Pressure Waveform ◽  
The Mean ◽  
Mimic Iii

Blood pressure (BP) monitoring has significant importance in the treatment of hypertension and different cardiovascular health diseases. As photoplethysmogram (PPG) signals can be recorded non-invasively, research has been highly conducted to measure BP using PPG recently. In this paper, we propose a U-net deep learning architecture that uses fingertip PPG signal as input to estimate arterial BP (ABP) waveform non-invasively. From this waveform, we have also measured systolic BP (SBP), diastolic BP (DBP), and mean arterial pressure (MAP). The proposed method was evaluated on a subset of 100 subjects from two publicly available databases: MIMIC and MIMIC-III. The predicted ABP waveforms correlated highly with the reference waveforms and we have obtained an average Pearson’s correlation coefficient of 0.993. The mean absolute error is 3.68 ± 4.42 mmHg for SBP, 1.97 ± 2.92 mmHg for DBP, and 2.17 ± 3.06 mmHg for MAP which satisfy the requirements of the Association for the Advancement of Medical Instrumentation (AAMI) standard and obtain grade A according to the British Hypertension Society (BHS) standard. The results show that the proposed method is an efficient process to estimate ABP waveform directly using fingertip PPG.

scholarly journals Subcritical Transmission in the Early Stage of COVID-19 in Korea

2021 ◽  
Vol 18 (3) ◽  
pp. 1265
Author(s):  
Yong Sul Won ◽  
Jong-Hoon Kim ◽  
Chi Young Ahn ◽  
Hyojung Lee
Keyword(s):  
Incubation Period ◽  
Early Stage ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Contact Tracing ◽  
Statistical Characterization ◽  
Serial Interval ◽  
Imported Cases ◽  
The Mean ◽  
Reporting Delays

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

scholarly journals Helium, [Fe/H] Abundances and the HR (Log TEFF, MBol) Diagram With Hipparcos Data of The Four Nearest Open Clusters: Hyades, Coma Berenices, The Pleiades and Praesepe

1998 ◽  
Vol 11 (1) ◽  
pp. 565-565
Author(s):  
G. Cayrel de Strobel ◽  
R. Cayrel ◽  
Y. Lebreton
Keyword(s):  
Main Sequence ◽  
Open Clusters ◽  
Main Sequence Stars ◽  
Spectroscopic Analyses ◽  
Solar Metallicity ◽  
Metal Abundances ◽  
The Mean ◽  
The Moment ◽  
The One ◽  
Best Fit

After having studied in great detail the observational HR diagram (log Teff, Mbol) composed by 40 main sequence stars of the Hyades (Perryman et al.,1997, A&A., in press), we have tried to apply the same method to the observational main sequences of the three next nearest open clusters: Coma Berenices, the Pleiades, and Praesepe. This method consists in comparing the observational main sequence of the clusters with a grid of theoretical ZAMSs. The stars composing the observational main sequences had to have reliable absolute bolometric magnitudes, coming all from individual Hipparcos parallaxes, precise bolometric corrections, effective temperatures and metal abundances from high resolution detailed spectroscopic analyses. If we assume, following the work by Fernandez et al. (1996, A&A,311,127), that the mixing-lenth parameter is solar, the position of a theoretical ZAMS, in the (log Teff, Mbol) plane, computed with given input physics, only depends on two free parameters: the He content Y by mass, and the metallicity Z by mass. If effective temperature and metallicity of the constituting stars of the 4 clusters are previously known by means of detailed analyses, one can deduce their helium abundances by means of an appropriate grid of theoretical ZAMS’s. The comparison between the empirical (log Teff, Mbol) main sequence of the Hyades and the computed ZAMS corresponding to the observed metallicity Z of the Hyades (Z= 0.0240 ± 0.0085) gives a He abundance for the Hyades, Y= 0.26 ± 0.02. Our interpretation, concerning the observational position of the main sequence of the three nearest clusters after the Hyades, is still under way and appears to be greatly more difficult than for the Hyades. For the moment we can say that: ‒ The 15 dwarfs analysed in detailed in Coma have a solar metallicity: [Fe/H] = -0.05 ± 0.06. However, their observational main sequence fit better with the Hyades ZAMS. ‒ The mean metallicity of 13 Pleiades dwarfs analysed in detail is solar. A metal deficient and He normal ZAMS would fit better. But, a warning for absorption in the Pleiades has to be recalled. ‒ The upper main sequence of Praesepe, (the more distant cluster: 180 pc) composed by 11 stars, analysed in detail, is the one which has the best fit with the Hyades ZAMS. The deduced ‘turnoff age’ of the cluster is slightly higher than that of the Hyades: 0.8 Gyr instead of 0.63 Gyr.

scholarly journals INFLUENCE OF STATISTICAL FLUCTUATIONS ON K/π RATIOS IN RELATIVISTIC HEAVY ION COLLISIONS

2001 ◽  
Vol 16 (07) ◽  
pp. 1227-1235 ◽  
Author(s):  
C. B. YANG ◽  
X. CAI
Keyword(s):  
Negative Binomial ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Relative Variance ◽  
Ion Collisions ◽  
Statistical Fluctuations ◽  
Binomial Distributions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
Statistical Background

The influence of pure statistical fluctuations on K/π ratio is investigated in an event-by-event way. Poisson and the modified negative binomial distributions are used as the multiplicity distributions since they both have statistical background. It is shown that the distributions of the ratio in these cases are Gaussian, and the mean and relative variance are given analytically.

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