On the equivalence of limit distributions of a sum and of a maximum sum of independent random variables

2010 ◽  
Vol 80 (9-10) ◽  
pp. 860-863 ◽  
Author(s):  
M. Sreehari
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Limit Distributions

Limit distributions of the Pearson statistics for nonhomogeneous polynomial scheme

2019 ◽  
Vol 29 (4) ◽  
pp. 233-239
Author(s):  
Maxim P. Savelov
Keyword(s):  
Quadratic Form ◽  
Normal Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Standard Normal Distribution ◽  
Limit Distributions ◽  
Standard Normal ◽  
Polynomial Scheme

Abstract For a nonhomogeneous polynomial scheme, conditions are found under which the Pearson statistic distributions converge to the distribution of nonnegative quadratic form of independent random variables with the standard normal distribution.

Nongaussian Limit Distributions of Lacunary Trigonometric Series

1991 ◽  
Vol 43 (5) ◽  
pp. 948-959 ◽  
Author(s):  
I. Berkes
Keyword(s):  
Asymptotic Behavior ◽  
Large Class ◽  
Trigonometric Series ◽  
Gaussian Distribution ◽  
Critical Speed ◽  
Random Variables ◽  
Independent Random Variables ◽  
Lacunary Trigonometric Series ◽  
Limit Distributions ◽  
Dependent Domain

AbstractIt is a well known fact that for rapidly increasing nkthe sequence , behaves like a sequence of independent random variables; in particular has a limiting Gaussian distribution as N → ∞. Under a certain critical speed this result breaks down and becomes strongly dependent. The purpose of this paper is to investigate the asymptotic behavior of normed sums in the strongly dependent domain; specifically, we construct a large class of nongaussian limit distributions of such sums.

Limit Distributions for Sums of Independent Random Variables.

1955 ◽  
Vol 118 (2) ◽  
pp. 248 ◽  
Author(s):  
D. V. Lindley ◽  
B. V. Gnedenko ◽  
A. N. Kolmogorov ◽  
K. L. Chung
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Limit Distributions

Limit Distributions for Sums of Independent Random Variables.

Biometrika ◽  
1963 ◽  
Vol 50 (1/2) ◽  
pp. 223
Author(s):  
D. E. Barton ◽  
B. V. Gmedenko ◽  
A. N. Kolmogorov ◽  
K. L. Chung
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Limit Distributions

Limit Distributions for Sums of Independent Random Variables.

1955 ◽  
Vol 50 (272) ◽  
pp. 1343
Author(s):  
Wassily Hoeffding ◽  
B. V. Gnedenko ◽  
A. N. Kolmogorov ◽  
K. L. Chung ◽  
J. L. Doob
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Limit Distributions
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