Distributions of ratios of random variables from the power-quadratic exponential family and applications

Statistics ◽  
2005 ◽  
Vol 39 (4) ◽  
pp. 355-372 ◽  
Author(s):  
T. Pham-Gia ◽  
N. Turkkan
Keyword(s):  
Exponential Family ◽  
Random Variables ◽  
Ratios Of Random Variables

Characterizations via conditional distributions

1977 ◽  
Vol 14 (04) ◽  
pp. 806-816
Author(s):  
Robert H. Berk
Keyword(s):  
Order Statistics ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Exponential Family ◽  
Random Variables ◽  
Independent Random Variables ◽  
Conditional Distributions

For independent random variablesXandY,if the conditional distribution ofXgivenX+Ysatisfies certain conditions, then the joint distribution ofXandYis a member of a certain one-parameter exponential family. Extensions fornindependent random variables are given. A characterization for independent random variables involving order statistics is also given.

ASYMPTOTIC BAYES ANALYSIS FOR THE FINITE-HORIZON ONE-ARMED-BANDIT PROBLEM

2003 ◽  
Vol 17 (1) ◽  
pp. 53-82 ◽  
Author(s):  
Apostolos N. Burnetas ◽  
Michael N. Katehakis
Keyword(s):  
Exponential Family ◽  
Random Variables ◽  
Finite Horizon ◽  
Optimization Under Uncertainty ◽  
Bandit Problem ◽  
Trade Off ◽  
Basic Model ◽  
Optimal Policies ◽  
Bayes Analysis ◽  
The One

The multiarmed-bandit problem is often taken as a basic model for the trade-off between the exploration and utilization required for efficient optimization under uncertainty. In this article, we study the situation in which the unknown performance of a new bandit is to be evaluated and compared with that of a known one over a finite horizon. We assume that the bandits represent random variables with distributions from the one-parameter exponential family. When the objective is to maximize the Bayes expected sum of outcomes over a finite horizon, it is shown that optimal policies tend to simple limits when the length of the horizon is large.

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