Random discrete distributions invariant under size-biased permutation

1996 ◽  
Vol 28 (02) ◽  
pp. 525-539 ◽  
Author(s):  
Jim Pitman
Keyword(s):  
Discrete Distribution ◽  
Parameter Family ◽  
Discrete Distributions ◽  
Finite Dimensional ◽  
Dirichlet Distributions ◽  
Two Parameter ◽  
Generalized Dirichlet

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under size-biased permutation. Apart from some exceptional cases and minor modifications, such models form a two-parameter family of generalized Dirichlet distributions.

Random discrete distributions invariant under size-biased permutation

1996 ◽  
Vol 28 (2) ◽  
pp. 525-539 ◽  
Author(s):  
Jim Pitman
Keyword(s):  
Discrete Distribution ◽  
Parameter Family ◽  
Discrete Distributions ◽  
Finite Dimensional ◽  
Dirichlet Distributions ◽  
Two Parameter ◽  
Generalized Dirichlet

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under size-biased permutation. Apart from some exceptional cases and minor modifications, such models form a two-parameter family of generalized Dirichlet distributions.

scholarly journals Characterizations of Twenty (2020-2021) Proposed Discrete Distributions

2021 ◽  
pp. 847-884
Author(s):  
G.G. Hamedani ◽  
Mahrokh Najaf ◽  
Amin Roshani ◽  
Nadeem Shafique Butt
Keyword(s):  
Exponential Distribution ◽  
Poisson Distribution ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Gumbel Distribution ◽  
Rayleigh Distribution ◽  
Discrete Distributions ◽  
Lindley Distribution ◽  
Lomax Distribution ◽  
Two Parameter

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter

scholarly journals Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type

10.37236/933 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Gregg Musiker ◽  
James Propp
Keyword(s):  
Lie Algebras ◽  
Cluster Algebras ◽  
Laurent Polynomials ◽  
Finite Dimensional ◽  
Combinatorial Interpretations ◽  
Rank 2 ◽  
The Individual ◽  
Affine Type ◽  
Positive Integers ◽  
Two Parameter

Fomin and Zelevinsky show that a certain two-parameter family of rational recurrence relations, here called the $(b,c)$ family, possesses the Laurentness property: for all $b,c$, each term of the $(b,c)$ sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers $b,c$ satisfy $bc < 4$, the recurrence is related to the root systems of finite-dimensional rank $2$ Lie algebras; when $bc>4$, the recurrence is related to Kac-Moody rank $2$ Lie algebras of general type. Here we investigate the borderline cases $bc=4$, corresponding to Kac-Moody Lie algebras of affine type. In these cases, we show that the Laurent polynomials arising from the recurence can be viewed as generating functions that enumerate the perfect matchings of certain graphs. By providing combinatorial interpretations of the individual coefficients of these Laurent polynomials, we establish their positivity.

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