TH-C-L100J-04: Reproducibility of Intra-Fractional Lung Motion Probability Distribution Function (PDF) Using Dynamic MRI: Statistical Analysis

2007 ◽  
Vol 34 (6Part22) ◽  
pp. 2622-2622
Author(s):  
J Cai ◽  
P Read ◽  
S Benedict ◽  
J Larner ◽  
K Sheng
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Dynamic Mri ◽  
Lung Motion ◽  
Motion Probability

Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI

2006 ◽  
Vol 52 (2) ◽  
pp. 365-373 ◽  
Author(s):  
Jing Cai ◽  
Paul W Read ◽  
Talissa A Altes ◽  
Janelle A Molloy ◽  
James R Brookeman ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Dynamic Mri ◽  
Lung Motion ◽  
Motion Probability

scholarly journals A statistical analysis of the radio properties of a large sample of 374 optically selected quasars

1986 ◽  
Vol 119 ◽  
pp. 111-112
Author(s):  
Gopal Krishna ◽  
H. Steppe ◽  
T. Ghosh ◽  
L. Saripalli
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Probability Distribution ◽  
Distinctive Feature ◽  
Probability Distribution Function ◽  
Significant Variation ◽  
Rest Frame ◽  
Radio Spectrum ◽  
Large Sample

Using a large, unbiased sample of 374 optically selected QSOs, of which 54 are radio detected, we have computed for different redshift ranges the probability distribution function φ (R) of R defined as the ratio of monochromatic luminosities at 15 GHz and 2500 Å in the QSO's rest frame. A significant variation of φ (R) with redshift is noticed. At small redshifts (z < 0.5), the distinctive feature of φ (R) is a peak near R∼102, arising due to the QSOs having steep radio spectrum(αr<−0.5).

scholarly journals A Probabilistic Model for Maximum Rainfall Frequency Analysis

Water ◽  
2021 ◽  
Vol 13 (19) ◽  
pp. 2688
Author(s):  
Maurycy Ciupak ◽  
Bogdan Ozga-Zieliński ◽  
Tamara Tokarczyk ◽  
Jan Adamowski
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Goodness Of Fit ◽  
Precipitation Series ◽  
Probability Of Exceedance ◽  
Maximum Precipitation ◽  
Best Fitting ◽  
Selection Of

As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs–Beck test; (ii) checking for the random variable’s independence using the Wald–Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable’s stationarity using nonparametric tests, e.g., the Kruskal–Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher–Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson’s χ2 test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov–Smirnov test, the Anderson–Darling test, the Liao–Shimokawa test, and Kuiper’s test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz–Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz–Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

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