scholarly journals Various limit theorems for ratios from the uniform distribution

2016 ◽  
Vol 14 (1) ◽  
pp. 393-403 ◽  
Author(s):  
Yu Miao ◽  
Yan Sun ◽  
Rujun Wang ◽  
Manru Dong
Keyword(s):  
Order Statistics ◽  
Uniform Distribution ◽  
Limit Theorems ◽  
Weak Laws

AbstractIn this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.

scholarly journals Limit theorems for randomly selected adjacent order statistics from a Pareto distribution

2005 ◽  
Vol 2005 (21) ◽  
pp. 3427-3441 ◽  
Author(s):  
André Adler
Keyword(s):  
Order Statistics ◽  
Prior Distribution ◽  
Limit Theorems ◽  
Pareto Distribution ◽  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws ◽  
Selection Of

Consider independent and identically distributed random variables{Xnk,  1≤k≤m, n≥1}from the Pareto distribution. We randomly select two adjacent order statistics from each row,Xn(i)andXn(i+1), where1≤i≤m−1. Then, we test to see whether or not strong and weak laws of large numbers with nonzero limits for weighted sums of the random variablesXn(i+1)/Xn(i)exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.

Representations and limit theorems for extreme value distributions

1978 ◽  
Vol 15 (03) ◽  
pp. 639-644 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Stochastic Process ◽  
Order Statistics ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Canonical Representation ◽  
Extreme Value ◽  
Limiting Distribution ◽  
Extreme Value Distributions ◽  
Independent Identically Distributed

LetXn1≦Xn2≦ ··· ≦Xnndenote the order statistics from a sample ofnindependent, identically distributed random variables, and suppose that the variablesXnn, Xn,n–1, ···, when suitably normalized, have a non-trivial limiting joint distributionξ1,ξ2, ···, asn → ∞. It is well known that the limiting distribution must be one of just three types. We provide a canonical representation of the stochastic process {ξn,n≧ 1} in terms of exponential variables, and use this representation to obtain limit theorems forξnasn →∞.

scholarly journals Limit theorems for multivariate Brownian semistationary processes and feasible results

2019 ◽  
Vol 51 (03) ◽  
pp. 667-716
Author(s):  
Riccardo Passeggeri ◽  
Almut E. D. Veraart
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Laws Of Large Numbers ◽  
Stationary Increments ◽  
Large Numbers ◽  
Weak Laws

AbstractIn this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.

Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces

1982 ◽  
Vol 19 (01) ◽  
pp. 221-228 ◽  
Author(s):  
A. J. Stam
Keyword(s):  
Normal Distribution ◽  
Uniform Distribution ◽  
Total Variation ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Geometric Probability ◽  
High Dimensional ◽  
Standard Normal Distribution ◽  
Uniform Distributions ◽  
Standard Normal

If X = (X 1, · ··, Xn ) has uniform distribution on the sphere or ball in ℝ with radius a, then the joint distribution of , ···, k, converges in total variation to the standard normal distribution on ℝ. Similar results hold for the inner products of independent n-vectors. Applications to geometric probability are given.

Limit theorems for order statistics from exponentials

2016 ◽  
Vol 110 ◽  
pp. 51-57 ◽  
Author(s):  
Yu Miao ◽  
Rujun Wang ◽  
Andre Adler
Keyword(s):  
Order Statistics ◽  
Limit Theorems
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