On the Characterization of Distributions through the Properties of Conditional Expectations of Order Statistics

2005 ◽  
pp. 73-81
Author(s):  
I Bairamov ◽  
O Gebizlioglu
Keyword(s):  
Order Statistics ◽  
Characterization Of Distributions ◽  
Conditional Expectations

Some new approaches to probability distributions

1980 ◽  
Vol 12 (04) ◽  
pp. 903-921 ◽  
Author(s):  
S. Kotz ◽  
D. N. Shanbhag
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Representation Theorems ◽  
Practical Applications ◽  
New Approaches ◽  
Characterization Of Distributions ◽  
Stability Theorems ◽  
Conditional Expectations

We develop some approaches to the characterization of distributions of real-valued random variables, useful in practical applications, in terms of conditional expectations and hazard measures. We prove several representation theorems generalizing earlier results, and establish stability theorems for two general characteristics introduced in this paper.

Characterization of certain populations by independence of order statistics

1972 ◽  
Vol 9 (01) ◽  
pp. 224-230 ◽  
Author(s):  
János Galambos
Keyword(s):  
Order Statistics ◽  
New Method ◽  
Characteristic Functions ◽  
Characterization Of Distributions

A method, making use of characteristic functions, is presented to prove theorems on characterization of distributions by independence of order statistics. Since exact independence in practice is rarely achieved, much attention is being given in the literature to theorems on determining the distributions for which certain statistics are ‘almost’ independent. The technique of this new line of investigation is strongly dependent on the fact that for the case of exact independence there is a solution in terms of characteristic functions. The present work was guided by this fact. In addition to the new method, Theorem 2 appears to be new.

Sign in / Sign up

Export Citation Format

Share Document