Complete Asymptotic Expansions for the Maximum Deviation of the Empirical Density Function

1979 ◽  
Vol 23 (3) ◽  
pp. 475-489 ◽  
Author(s):  
V. D. Konakov
Keyword(s):  
Density Function ◽  
Asymptotic Expansions ◽  
Maximum Deviation ◽  
Empirical Density ◽  
Empirical Density Function

scholarly journals The asymptotic expansions of the distribution function and of density function for the sums of independent identically distributed random vectors

1968 ◽  
Vol 8 (3) ◽  
pp. 405-422
Author(s):  
A. Bikelis
Keyword(s):  
Distribution Function ◽  
Density Function ◽  
Asymptotic Expansions ◽  
Random Vectors ◽  
Independent Identically Distributed

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. Бикялис. Асимптотические разложения для плотностей и распределений сумм независимых одинаково распределенных случайных векторов A. Bikelis. Nepriklausomų vienodai pasiskirsčiusių atsitiktinių vektorių sumų tankių ir pasiskirstymo funkcijų asimptotiniai išdėstymai

Distribution of Variables Extracted from Spectral EEG-Analysis

1976 ◽  
Vol 15 (02) ◽  
pp. 94-98 ◽  
Author(s):  
G. Ferber ◽  
G. Eichholz
Keyword(s):  
Distribution Functions ◽  
Eeg Analysis ◽  
Natural Classification ◽  
Linear Discriminant ◽  
Important Group ◽  
Empirical Density ◽  
Kolmogorov Statistic ◽  
Two Peaks ◽  
Empirical Density Function

For 1000 variables extracted from auto- and cross-spectra of two 12-channel montages, the empirical density function is investigated. Only a small group of them may be considered to have a univariate normal distribution. Another important group including the absolute and the relative power in the four classical frequency bands has distribution functions that may be more or less accurately approximated by gamma-type functions.A third group including some of the peak frequencies shows distribution functions with two peaks not assignable to any natural classification of the EEG.The power of discrimination between the four samples is investigated for each variable by means of Bayes-classification and by a quasi-Kolmogorov-statistic. Its quality is demonstrated using linear discriminant analysis.Correlations were computed to complete basic statistical information.

scholarly journals Information Geometry of the Exponential Family of Distributions with Progressive Type-II Censoring

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 687
Author(s):  
Fode Zhang ◽  
Xiaolin Shi ◽  
Hon Keung Tony Ng
Keyword(s):  
Density Function ◽  
Asymptotic Expansions ◽  
Exponential Family ◽  
Information Geometry ◽  
Type Ii ◽  
Predictive Density ◽  
Progressive Type ◽  
Exponential Family Of Distributions ◽  
Progressive Type Ii Censoring ◽  
Family Of Distributions

In geometry and topology, a family of probability distributions can be analyzed as the points on a manifold, known as statistical manifold, with intrinsic coordinates corresponding to the parameters of the distribution. Consider the exponential family of distributions with progressive Type-II censoring as the manifold of a statistical model, we use the information geometry methods to investigate the geometric quantities such as the tangent space, the Fisher metric tensors, the affine connection and the α-connection of the manifold. As an application of the geometric quantities, the asymptotic expansions of the posterior density function and the posterior Bayesian predictive density function of the manifold are discussed. The results show that the asymptotic expansions are related to the coefficients of the α-connections and metric tensors, and the predictive density function is the estimated density function in an asymptotic sense. The main results are illustrated by considering the Rayleigh distribution.

scholarly journals Empirical Density Estimation for Interval Censored Data

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Eugenia Stoimenova
Keyword(s):  
Density Function ◽  
Density Estimation ◽  
Censored Data ◽  
Nonparametric Estimation ◽  
Kernel Density ◽  
Interval Data ◽  
Interval Censoring ◽  
Density Estimator ◽  
Interval Censored ◽  
Empirical Density

This paper is concerned with the nonparametric estimation of a density function when the data are incomplete due to interval censoring. The Nadaraya-Watson kernel density estimator is modified to allow description of such interval data. An interactive R application is developed to explore different estimates.

The structure of amorphous and polycrystalline materials using energy-filtered RDF analysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1190-1191
Author(s):  
David Cockayne ◽  
David McKenzie
Keyword(s):  
Electron Diffraction ◽  
Diffraction Pattern ◽  
Density Function ◽  
Electron Diffraction Pattern ◽  
Polycrystalline Materials ◽  
Nearest Neighbour ◽  
X Ray ◽  
Selected Area Electron Diffraction ◽  
Reduced Density ◽  
System F

The technique of Electron Reduced Density Function (RDF) analysis has ben developed into a rapid analytical tool for the analysis of small volumes of amorphous or polycrystalline materials. The energy filtered electron diffraction pattern is collected to high scattering angles (currendy to s = 2 sinθ/λ = 6.5 Å-1) by scanning the selected area electron diffraction pattern across the entrance aperture to a GATAN parallel energy loss spectrometer. The diffraction pattern is then converted to a reduced density function, G(r), using mathematical procedures equivalent to those used in X-ray and neutron diffraction studies.Nearest neighbour distances accurate to 0.01 Å are obtained routinely, and bond distortions of molecules can be determined from the ratio of first to second nearest neighbour distances. The accuracy of coordination number determinations from polycrystalline monatomic materials (eg Pt) is high (5%). In amorphous systems (eg carbon, silicon) it is reasonable (10%), but in multi-element systems there are a number of problems to be overcome; to reduce the diffraction pattern to G(r), the approximation must be made that for all elements i,j in the system, fj(s) = Kji fi,(s) where Kji is independent of s.

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