A Hoffmann-Jørgensen inequality of NA random variables with applications to the convergence rate

2013 ◽  
pp. 313-328
Author(s):  
Xiaorong Yang ◽  
Ke-Ang Fu
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Na Random Variables

The Hájek–Rényi inequality for the NA random variables and its application

1999 ◽  
Vol 44 (2) ◽  
pp. 210 ◽  
Author(s):  
Jingjun Liu ◽  
Shixin Gan ◽  
Pingyan Chen
Keyword(s):  
Random Variables ◽  
Na Random Variables

scholarly journals Tail Properties and Asymptotic Expansions for the Maximum of the Logarithmic Skew-Normal Distribution

2013 ◽  
Vol 50 (3) ◽  
pp. 900-907 ◽  
Author(s):  
Xin Liao ◽  
Zuoxiang Peng ◽  
Saralees Nadarajah
Keyword(s):  
Asymptotic Expansion ◽  
Convergence Rate ◽  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal

We discuss tail behaviors, subexponentiality, and the extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. We show that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distribution is proportional to 1/(log n)1/2.

scholarly journals On the Bahadur representation of sample quantiles for widely orthant dependent sequences

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1333-1343 ◽  
Author(s):  
Wenzhi Yang ◽  
Tingting Liu ◽  
Xuejun Wang ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Bahadur Representation ◽  
Negatively Associated ◽  
Statistics And Probability ◽  
Na Random Variables ◽  
End Random Variables ◽  
Widely Orthant Dependent ◽  
Na Sequences ◽  
Nod Sequence ◽  
Sample Quantiles

It can be found that widely orthant dependent (WOD) random variables are weaker than extended negatively orthant dependent (END) random variables, while END random variables are weaker than negatively orthant dependent (NOD) and negatively associated (NA) random variables. In this paper, we investigate the Bahadur representation of sample quantiles based on WOD sequences. Our results extend the corresponding ones of Ling [N.X. Ling, The Bahadur representation for sample quantiles under negatively associated sequence, Statistics and Probability Letters 78(16) (2008), 2660-2663], Xu et al. [S.F. Xu, L. Ge, Y. Miao, On the Bahadur representation of sample quantiles and order statistics for NA sequences, Journal of the Korean Statistical Society 42(1) (2013), 1-7] and Li et al. [X.Q. Li, W.Z. Yang, S.H. Hu, X.J. Wang, The Bahadur representation for sample quantile under NOD sequence, Journal of Nonparametric Statistics 23(1) (2011), 59-65] for the case of NA sequences or NOD sequences.

The geometric convergence rate of a Lindley random walk

1997 ◽  
Vol 34 (3) ◽  
pp. 806-811
Author(s):  
Robert B. Lund
Keyword(s):  
Random Walk ◽  
Convergence Rate ◽  
Large Deviations ◽  
Total Variation ◽  
Short Proof ◽  
Random Variables ◽  
Invariant Distribution ◽  
Initial State ◽  
Geometric Convergence ◽  
Independent And Identically Distributed

Let {Xn} be the Lindley random walk on [0,∞) defined by . Here, {An} is a sequence of independent and identically distributed random variables. When for some r > 1, {Xn} converges at a geometric rate in total variation to an invariant distribution π; i.e. there exists s > 1 such that for every initial state . In this communication we supply a short proof and some extensions of a large deviations result initially due to Veraverbeke and Teugels (1975, 1976): the largest s satisfying the above relationship is and satisfies φ ‘(r0) = 0.

Sign in / Sign up

Export Citation Format

Share Document