The increments of partial sums of a dependent sequence when the moment generating functions do not exist

1989 ◽  
Vol 5 (4) ◽  
pp. 289-296 ◽  
Author(s):  
Lin Zhengyan
Keyword(s):  
Generating Functions ◽  
Partial Sums ◽  
Dependent Sequence ◽  
Moment Generating Functions ◽  
The Moment

The Properties Related to the Moment Generating Function of the Fuzzy Variable

2014 ◽  
Vol 519-520 ◽  
pp. 863-866
Author(s):  
Sheng Ma
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Uncertainty Theory ◽  
Fuzzy Variable ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Moment Generating Functions ◽  
The Moment

In the paper, some properties related to the moment generating function of a fuzzy variable are discussed based on uncertainty theory. And we obtain the result that the convergence of moment generating functions to an moment generating function implies convergence of credibility distribution functions. Thats, the moment generating function characterizes a credibility distribution.

scholarly journals Quasimodularity of the kth residual cranks

2020 ◽  
pp. 1-13
Author(s):  
Thomas Morrill ◽  
Aleksander Simonič
Keyword(s):  
Generating Functions ◽  
Second Moments ◽  
Moment Generating Functions ◽  
The Moment

We study a family of residual crank generating functions defined on overpartitions, the so-called [Formula: see text]th residual cranks. Specifically, the moment generating functions associated to these cranks exhibit quasimodularity properties which are dependent on the choice of [Formula: see text]. We also show that the second moments of these cranks admit a combinatoric interpretation as weighted overpartition counts. This interpretation gives a refinement to an existing inequality between crank moments of differing modulus [Formula: see text].

The structured coalescent process with weak migration

2001 ◽  
Vol 38 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Migration Rates ◽  
Structured Population ◽  
Moment Generating Functions ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

The structured coalescent process with weak migration

2001 ◽  
Vol 38 (01) ◽  
pp. 1-17 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Migration Rates ◽  
Structured Population ◽  
Moment Generating Functions ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

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