Tests of Fit for Wrapped Stable Distributions Based on the Characteristic Function

2021 ◽  
pp. 383-398
Author(s):  
Simos G. Meintanis ◽  
S. Rao Jammalamadaka ◽  
Qianyu Jin
Keyword(s):  
Characteristic Function ◽  
Stable Distributions ◽  
Tests Of Fit

The characteristic functions of functions

1968 ◽  
Vol 307 (1490) ◽  
pp. 317-334 ◽  
Keyword(s):  
Multivariate Analysis ◽  
Characteristic Function ◽  
Gaussian Model ◽  
Random Variable ◽  
Stable Distributions ◽  
Characteristic Functions ◽  
Real Characteristic ◽  
Vector Random Variable

The characteristic functions of various functions of a real or vector random variable are expressed in terms of the characteristic function of that variable. In the examples there is special emphasis on the stable distributions that have real characteristic functions. Some of the results suggest the practicability of generalizing traditional multivariate analysis beyond the multi-Gaussian model.

scholarly journals A direct approach to the stable distributions

2016 ◽  
Vol 48 (A) ◽  
pp. 261-282 ◽  
Author(s):  
E. J. G. Pitman ◽  
Jim Pitman
Keyword(s):  
Functional Equation ◽  
Characteristic Function ◽  
Integral Representation ◽  
Explicit Form ◽  
Regular Variation ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Direct Approach ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

AbstractThe explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying the theory of regular variation, without appeal to the general Lévy‒Khintchine integral representation of infinitely divisible distributions.

scholarly journals A Characterization of Symmetric Stable Distributions

2016 ◽  
Vol 2016 ◽  
pp. 1-3
Author(s):  
Wiktor Ejsmont
Keyword(s):  
Characteristic Function ◽  
Normal Distribution ◽  
Linear Form ◽  
Stable Distributions

Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions.

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