Bounds on the distance of a mixture from its parent distribution

1981 ◽  
Vol 18 (4) ◽  
pp. 853-863 ◽  
Author(s):  
Moshe Shaked
Keyword(s):  
Upper Bounds ◽  
New Technique ◽  
Scale Mixture ◽  
Uniform Distance ◽  
Parent Distribution

In a series of recent papers, Heyde (1975), Heyde and Leslie (1976), Hall (1979) and Brown (1980) obtained upper bounds on the uniform distance of a scale mixture from its parent distribution. Using a different technique we obtain further bounds which are more meaningful and superior in some applications. The new technique is then applied to obtain bounds on the uniform distance of a location mixture from its parent distribution. Comparison of the new bounds and the earlier ones is given.

Bounds on the distance of a mixture from its parent distribution

1981 ◽  
Vol 18 (04) ◽  
pp. 853-863
Author(s):  
Moshe Shaked
Keyword(s):  
Upper Bounds ◽  
New Technique ◽  
Scale Mixture ◽  
Uniform Distance ◽  
Parent Distribution

In a series of recent papers, Heyde (1975), Heyde and Leslie (1976), Hall (1979) and Brown (1980) obtained upper bounds on the uniform distance of a scale mixture from its parent distribution. Using a different technique we obtain further bounds which are more meaningful and superior in some applications. The new technique is then applied to obtain bounds on the uniform distance of a location mixture from its parent distribution. Comparison of the new bounds and the earlier ones is given.

scholarly journals New continuity estimates of geometric sums

2002 ◽  
Vol 15 (3) ◽  
pp. 219-233 ◽  
Author(s):  
Evgueni Gordienko ◽  
Juan Ruiz de Chávez
Keyword(s):  
Stochastic Models ◽  
Random Number ◽  
Random Variables ◽  
Upper Bounds ◽  
Uniform Distance ◽  
Right Hand ◽  
The Stability ◽  
The Right ◽  
Geometric Sums ◽  
Independent And Identically Distributed

The paper deals with sums of a random number of independent and identically distributed random variables. More specifically, we compare two such sums, which differ from each other in the distributions of their summands. New upper bounds (inequalities) for the uniform distance between distributions of sums are established. The right-hand sides of these inequalities are expressed in terms of Zolotarev's and the uniform distances between the distributions of summands. Such a feature makes it possible to consider these inequalities as continuity estimates and to apply them to the study of the stability (continuity) of various applied stochastic models involving geometric sums and their generalizations.

scholarly journals Upper Bounds for the Capacity for Severely Fading MIMO Channels under a Scale Mixture Assumption

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 845
Author(s):  
Johannes T. Ferreira
Keyword(s):  
Wireless Communication ◽  
Normal Distribution ◽  
Arbitrary Number ◽  
Mimo Systems ◽  
Upper Bounds ◽  
Complex Matrix ◽  
Scale Mixture ◽  
Mimo Channels ◽  
Underlying Distribution ◽  
Propagation Matrix

A cornerstone in the modeling of wireless communication is MIMO systems, where a complex matrix variate normal assumption is often made for the underlying distribution of the propagation matrix. A popular measure of information, namely capacity, is often investigated for the performance of MIMO designs. This paper derives upper bounds for this measure of information for the case of two transmitting antennae and an arbitrary number of receiving antennae when the propagation matrix is assumed to follow a scale mixture of complex matrix variate normal distribution. Furthermore, noncentrality is assumed to account for LOS scenarios within the MIMO environment. The insight of this paper illustrates the theoretical form of capacity under these key assumptions and paves the way for considerations of alternative distributional choices for the channel propagation matrix in potential cases of severe fading, when the assumption of normality may not be realistic.

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