A Characterization of a Polya-Eggenberger and Other Discrete Distributions by Record Values.

1980 ◽  
Author(s):  
Ramesh M. Korwar
Keyword(s):  
Record Values ◽  
Discrete Distributions

The characterization of distributions by order statistics and record values — a unified approach

1984 ◽  
Vol 21 (2) ◽  
pp. 326-334 ◽  
Author(s):  
Paul Deheuvels
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Simple Proof ◽  
Order Statistic ◽  
Continuous Distribution ◽  
Record Values ◽  
Discrete Distributions ◽  
Unified Approach ◽  
Characterization Of Distributions

It is shown that, in some particular cases, it is equivalent to characterize a continuous distribution by properties of records and by properties of order statistics. As an application, we give a simple proof that if two successive jth record values and associated to an i.i.d. sequence are such that and are independent, then the sequence has to derive from an exponential distribution (in the continuous case). The equivalence breaks up for discrete distributions, for which we give a proof that the only distributions such that Xk, n and Xk+1, n – Xk, n are independent for some k ≧ 2 (where Xk, n is the kth order statistic of X1, ···, Xn) are degenerate.

The characterization of distributions by order statistics and record values — a unified approach

1984 ◽  
Vol 21 (02) ◽  
pp. 326-334
Author(s):  
Paul Deheuvels
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Simple Proof ◽  
Order Statistic ◽  
Continuous Distribution ◽  
Record Values ◽  
Discrete Distributions ◽  
Unified Approach ◽  
Characterization Of Distributions

It is shown that, in some particular cases, it is equivalent to characterize a continuous distribution by properties of records and by properties of order statistics. As an application, we give a simple proof that if two successivejth record valuesandassociated to an i.i.d. sequence are such thatandare independent, then the sequence has to derive from an exponential distribution (in the continuous case). The equivalence breaks up for discrete distributions, for which we give a proof that the only distributions such thatXk, nandXk+1,n–Xk, nare independent for somek≧ 2 (whereXk, nis thekth order statistic ofX1, ···,Xn) are degenerate.

Characterization of discrete distributions using expected values

1995 ◽  
Vol 36 (1) ◽  
Author(s):  
J. M. Ruiz ◽  
J. Navarro
Keyword(s):  
Discrete Distributions ◽  
Expected Values

A Characterization of the Gumbel Distribution Based on Record Values

2003 ◽  
Vol 32 (11) ◽  
pp. 2101-2108 ◽  
Author(s):  
A. A. AlZaid ◽  
M. Ahsanullah
Keyword(s):  
Gumbel Distribution ◽  
Record Values

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332 ◽  
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

On characterizing discrete distributions via conditional expectations of weak record values

Metrika ◽  
2006 ◽  
Vol 66 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Katarzyna Danielak ◽  
Anna Dembińska
Keyword(s):  
Record Values ◽  
Discrete Distributions ◽  
Conditional Expectations
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