An Elementary Characterization of Weak Convergence of Measures

1985 ◽  
Vol 92 (2) ◽  
pp. 136 ◽  
Author(s):  
Jerry Johnson
Keyword(s):  
Weak Convergence ◽  
Weak Convergence Of Measures ◽  
Elementary Characterization

On weak convergence within the hnbue family of life distributions

1984 ◽  
Vol 21 (03) ◽  
pp. 654-660 ◽  
Author(s):  
Sujit K. Basu ◽  
Manish C. Bhattacharjee
Keyword(s):  
Weak Convergence ◽  
Exponential Distribution ◽  
Limiting Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moment Sequence ◽  
Positive Order ◽  
Life Distributions ◽  
Necessary And Sufficient

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

scholarly journals Rapid variation with remainder and rates of convergence

1990 ◽  
Vol 22 (04) ◽  
pp. 787-801 ◽  
Author(s):  
J. Beirlant ◽  
E. Willekens
Keyword(s):  
Weak Convergence ◽  
Asymptotic Behaviour ◽  
Rates Of Convergence ◽  
Convergence Result ◽  
Hill Estimator ◽  
Rapid Variation ◽  
Double Exponential Distribution ◽  
Double Exponential ◽  
The Hill

In this paper, we refine the concept of Γ-variation up to second order, and we give a characterization of this type of asymptotic behaviour. We apply our results to obtain uniform rates of convergence in the weak convergence of renormalised sample maxima to the double exponential distribution. In a second application we derive a rate of convergence result for the Hill estimator.

scholarly journals An elementary characterization of the Gini index

2015 ◽  
Vol 74 ◽  
pp. 79-83 ◽  
Author(s):  
L. Plata-Pérez ◽  
J. Sánchez-Pérez ◽  
F. Sánchez-Sánchez
Keyword(s):  
Gini Index ◽  
Elementary Characterization

scholarly journals Weak convergence of measures

Metrika ◽  
1984 ◽  
Vol 31 (1) ◽  
pp. 284-284
Author(s):  
E. Siebert
Keyword(s):  
Weak Convergence ◽  
Weak Convergence Of Measures

On an elementary characterization of the increasing convex ordering, by an application

1994 ◽  
Vol 31 (3) ◽  
pp. 834-840 ◽  
Author(s):  
Armand M. Makowski
Keyword(s):  
Short Proof ◽  
Probability Distributions ◽  
Short Note ◽  
Comparison Result ◽  
Convex Ordering ◽  
Simple Characterization ◽  
Increasing Convex Ordering ◽  
Elementary Characterization

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

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