Affine relation between an infinitely divisible distribution function and its Lévy measure

2021 ◽  
Vol 499 (2) ◽  
pp. 125008
Author(s):  
Anthony G. Pakes
Keyword(s):  
Distribution Function ◽  
Divisible Distribution ◽  
Infinitely Divisible Distribution ◽  
Lévy Measure ◽  
Infinitely Divisible

Max-infinite divisibility and multivariate total positivity

1994 ◽  
Vol 31 (3) ◽  
pp. 721-730 ◽  
Author(s):  
Abdulhamid A. Alzaid ◽  
Frank Proschan
Keyword(s):  
Distribution Function ◽  
Total Positivity ◽  
Positive Function ◽  
Infinite Divisibility ◽  
Divisible Distribution ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
Positive Dependence ◽  
Totally Positive

The concept of max-infinite divisibility is viewed as a positive dependence concept. It is shown that every max-infinitely divisible distribution function is a multivariate totally positive function of order 2 (MTP2). Inequalities are derived, with emphasis on exchangeable distributions. Applications and examples are given throughout the paper.

scholarly journals SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY

2020 ◽  
pp. 1-24 ◽  
Author(s):  
TOSHIRO WATANABE
Keyword(s):  
Asymptotic Behaviour ◽  
Real Line ◽  
Infinite Divisibility ◽  
Second Order ◽  
Divisible Distribution ◽  
Infinitely Divisible Distribution ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Exponential Moment ◽  
The Real

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we study the second order asymptotic behaviour of the tail of the $t$ th convolution power of an infinitely divisible distribution. The density version for a self-decomposable distribution on the real line without an exponential moment assumption is also given. Finally, the regularly varying case for a self-decomposable distribution on the half line is discussed.

Max-infinite divisibility and multivariate total positivity

1994 ◽  
Vol 31 (03) ◽  
pp. 721-730 ◽  
Author(s):  
Abdulhamid A. Alzaid ◽  
Frank Proschan
Keyword(s):  
Distribution Function ◽  
Total Positivity ◽  
Positive Function ◽  
Infinite Divisibility ◽  
Divisible Distribution ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
Positive Dependence ◽  
Totally Positive

The concept of max-infinite divisibility is viewed as a positive dependence concept. It is shown that every max-infinitely divisible distribution function is a multivariate totally positive function of order 2 (MTP2). Inequalities are derived, with emphasis on exchangeable distributions. Applications and examples are given throughout the paper.

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