Characterizations of discrete distributions based on conditional expectations of record values

2001 ◽  
Vol 42 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Manuel Franco ◽  
José M. Ruiz
Keyword(s):  
Record Values ◽  
Discrete Distributions ◽  
Conditional Expectations

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

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.

scholarly journals Some Characterization and Relations Based on K-th Lower Record Values

2016 ◽  
Vol 7 (1) ◽  
pp. 36-44
Author(s):  
Ali A. Al-Shomrani
Keyword(s):  
Conditional Expectation ◽  
Recurrence Relations ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Record Values ◽  
Distribution Functions ◽  
Conditional Expectations ◽  
Lower Record ◽  
Lower Record Values ◽  
Necessary And Sufficient

In this paper, we obtain certain expressions and recurrence relations for two general classes of distributions based on some conditional expectations of k-th lower record values. We consider the necessary and sufficient conditions such that these conditional expectations hold for some distribution functions. Furthermore, an expression of conditional expectation of other general class of distributions through truncated moments of some random variable is considered. Some distributions as examples of these general classes are shown in Tables1and2accordingly.

Some results on conditional expectations of lower record values

Statistics ◽  
2011 ◽  
Vol 45 (3) ◽  
pp. 237-255 ◽  
Author(s):  
Mahdi Tavangar ◽  
Majid Asadi
Keyword(s):  
Record Values ◽  
Conditional Expectations ◽  
Lower Record ◽  
Lower Record Values
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