scholarly journals A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chris Sherlock ◽  
Daniel Elton
Keyword(s):  
Functional Form ◽  
Marginal Distribution ◽  
Random Variables ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Symmetric Distributions ◽  
One Dimensional ◽  
Elliptically Symmetric Distributions

We present a class of spherically symmetric random variables defined by the property that as dimension increases to infinity the mass becomes concentrated in a hyperspherical shell, the width of which is negligible compared to its radius. We provide a sufficient condition for this property in terms of the functional form of the density and then show that the property carries through to equivalent elliptically symmetric distributions, provided that the contours are not too eccentric, in a sense which we make precise. Individual components of such distributions possess a number of appealing Gaussian-like limit properties, in particular that the limiting one-dimensional marginal distribution along any component is Gaussian.

scholarly journals SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

2012 ◽  
Vol 26 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Random Variables ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
Linear Combinations

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].

scholarly journals One-dimensional distributions of subordinators with upper truncated Lévy measure, and applications

2009 ◽  
Vol 41 (2) ◽  
pp. 367-392 ◽  
Author(s):  
Shai Covo
Keyword(s):  
Distribution Function ◽  
Lévy Process ◽  
Marginal Distribution ◽  
Levy Process ◽  
Gamma Process ◽  
Lévy Measure ◽  
Original Process ◽  
One Dimensional ◽  
Analogous Formula

Given a pure-jump subordinator (i.e. nondecreasing Lévy process with no drift) with continuous Lévy measure ν, we derive a formula for the distribution function Fs (x; t) at time t of the associated subordinator whose Lévy measure is the restriction of ν to (0,s]. It will be expressed in terms of ν and the marginal distribution function F (⋅; t) of the original process. A generalization concerning an arbitrary truncation of ν will follow. Under certain conditions, an analogous formula will be obtained for the nth derivative, ∂nFs (x; t) ∂ xn. The requirement that ν is continuous is shown to have no intrinsic meaning. A number of interesting results involving the size ordered jumps of subordinators will be derived. An appropriate approximation for the small jumps of a gamma process will be considered, leading to a revisiting of the generalized Dickman distribution.

scholarly journals Slepian-Bangs-type formulas and the related Misspecified Cramér-Rao Bounds for Complex Elliptically Symmetric distributions

2018 ◽  
Vol 142 ◽  
pp. 320-329 ◽  
Author(s):  
Abdelmalek Mennad ◽  
Stefano Fortunati ◽  
Mohammed Nabil El Korso ◽  
Arezki Younsi ◽  
Abdelhak M. Zoubir ◽  
...  
Keyword(s):  
Symmetric Distributions ◽  
Elliptically Symmetric Distributions
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