scholarly journals Modelling with star-shaped distributions

2020 ◽  
Vol 8 (1) ◽  
pp. 45-69
Author(s):  
Eckhard Liebscher ◽  
Wolf-Dieter Richter
Keyword(s):  
Probabilistic Models ◽  
Arbitrary Dimension ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Range ◽  
Gaussian Density ◽  
Spherical Distributions ◽  
Data Points ◽  
Non Gaussian ◽  
General Method

AbstractWe prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

Non-Gaussian clutter characterization applied to OTHR using a mixture of two Rayleigh probability density functions

2009 ◽  
Vol 44 (6) ◽  
pp. 663-666
Author(s):  
Steven C. Gustafson ◽  
Evan A. James ◽  
Andrew J. Terzuoli ◽  
Lindsay N. Weidenhammer ◽  
Rod I. Barnes
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Non Gaussian

scholarly journals The Poisson-Voronoi tessellation: relationships for edges

2005 ◽  
Vol 37 (2) ◽  
pp. 279-296 ◽  
Author(s):  
L. Muche
Keyword(s):  
Poisson Point Process ◽  
Arbitrary Dimension ◽  
Voronoi Tessellation ◽  
Probability Density Functions ◽  
Angular Distributions ◽  
Density Functions ◽  
Unified Approach ◽  
Distributional Properties ◽  
Dimensional Section ◽  
Lower Dimensional

In a unified approach, this paper presents distributional properties of a Voronoi tessellation generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the ‘typical’ edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poisson points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.

scholarly journals The Poisson-Voronoi tessellation: relationships for edges

2005 ◽  
Vol 37 (02) ◽  
pp. 279-296 ◽  
Author(s):  
L. Muche
Keyword(s):  
Poisson Point Process ◽  
Arbitrary Dimension ◽  
Voronoi Tessellation ◽  
Probability Density Functions ◽  
Angular Distributions ◽  
Density Functions ◽  
Unified Approach ◽  
Distributional Properties ◽  
Dimensional Section ◽  
Lower Dimensional

In a unified approach, this paper presents distributional properties of a Voronoi tessellation generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the ‘typical’ edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poisson points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.

The Effects of Cylinder Liner Finish on Piston Ring-Pack Friction

2004 ◽  
Author(s):  
Jeffrey Jocsak ◽  
Victor W. Wong ◽  
Tian Tian
Keyword(s):  
Surface Roughness ◽  
Probability Density ◽  
Piston Ring ◽  
Cylinder Liner ◽  
Probability Density Functions ◽  
Density Functions ◽  
Asperity Contact ◽  
Piston Ring Pack ◽  
Ring Pack ◽  
Non Gaussian

This paper presents enhancements to a previously developed mixed-lubrication ring-pack model that has been used extensively in the automotive industry in predicting piston-ring/liner oil film thickness, friction and oil-transport processes along the liner. The previous model considers three lubrication regimes, shear thinning of the lubricant, and the unsteady wetting conditions of the rings at the leading and trailing edges. The model incorporates the effects of surface roughness by using Patir and Cheng’s average flow model and the Greenwood and Tripp statistical asperity contact model, assuming a Gaussian distribution of surface roughness. However, as a result of the methods used to machine a cylinder liner and the wear-in process observed in engines, the cylinder liner finish is highly non-Gaussian. The purpose of this current study is to understand the effects of additional surface parameters other than Gaussian root-mean-square surface roughness on piston ring-pack friction in the context of a natural gas reciprocating engine ring/liner interface. In general, the surface roughness of a cylinder liner is negatively skewed. Applying similar methodology published in the literature, a wide variety of non-Gaussian probability density functions were generated in terms of the skewness of the cylinder liner surface. These probability density functions were implemented into the Greenwood and Tripp asperity contact model, and subsequently into the traditional MIT ring-pack friction model. The effects of surface skewness on flow were approximated using Gaussian flow factors and a simple truncation method. The enhanced model was studied in conjunction with results from an existing ring-pack dynamic model that provided the dynamic twists of the rings relative to the liner and inter-ring pressures. In this manner, a detailed analysis of the effects of engineered cylinder liner finish on reducing friction losses was performed.

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