Isotonic estimators of monotone densities and distribution functions: basic facts

1993 ◽  
Vol 47 (3) ◽  
pp. 175-183 ◽  
Author(s):  
P. Groeneboom ◽  
H. P. Lopuhaa
Keyword(s):  
Distribution Functions ◽  
Basic Facts ◽  
Monotone Densities

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

Obtaining Normalized Atomic Radial Distribution Functions from EELFS Spectra

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-577-C2-578 ◽  
Author(s):  
D. V. Surnin ◽  
D. E. Denisov ◽  
Yu. V. Ruts ◽  
P. M. Knjazev
Keyword(s):  
Radial Distribution ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Atomic Radial Distribution

Calculation of spatially inhomogeneous electron distribution functions

1998 ◽  
Vol 08 (PR7) ◽  
pp. Pr7-33-Pr7-42
Author(s):  
L. L. Alves ◽  
G. Gousset ◽  
C. M. Ferreira
Keyword(s):  
Electron Distribution ◽  
Distribution Functions ◽  
Spatially Inhomogeneous
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