A characterization of the Wishart exponential families by an invariance property

1989 ◽  
Vol 2 (1) ◽  
pp. 71-86 ◽  
Author(s):  
G�rard Letac
Keyword(s):  
Exponential Families ◽  
Invariance Property

A characterization of certain discrete exponential families

1996 ◽  
Vol 48 (3) ◽  
pp. 573-576 ◽  
Author(s):  
T. T. Nguyen ◽  
A. K. Gupta ◽  
Y. Wang
Keyword(s):  
Exponential Families

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (03) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

Characterization of multinomial exponential families by generalized variance

2010 ◽  
Vol 80 (11-12) ◽  
pp. 939-944 ◽  
Author(s):  
Abdelaziz Ghribi ◽  
Afif Masmoudi
Keyword(s):  
Exponential Families ◽  
Generalized Variance

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (3) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

scholarly journals On Chasles' Property of the Helicoid in Tri-Twisted Real Ambient Space

2015 ◽  
Vol 23 (2) ◽  
pp. 121-132
Author(s):  
Peter T. Ho ◽  
Lucy H. Odom ◽  
Bogdan D. Suceavă
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Arbitrary Point ◽  
Invariance Property ◽  
Elementary Property ◽  
Invariance Condition ◽  
Xixth Century ◽  
Rigidity Property ◽  
Three Dimensional Space

Abstract An elementary property of the helicoid is that at every point of the surface the following condition holds: cot θ = C · d; where d is the distance between an arbitrary point to the helicoid axis, and θ is the angle between the normal and the helicoid’s axis. This rigidity property was discovered by M. Chasles in the first half of the XIXth century. Starting from this property, we give a characterization of the so-called tri-twisted metrics on the real three dimensional space with the property that a given helicoid satisfies the classical invariance condition. Similar studies can be pursued in other geometric contexts. Our most general result presents a property of surfaces of rotation observing an invariance property suggested by the analogy with Chasles’s property.

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