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.

A perturbation method for the structured coalescent with strong migration

2000 ◽  
Vol 37 (1) ◽  
pp. 148-167 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Population Genetics ◽  
Perturbation Method ◽  
Dna Sequences ◽  
Generating Functions ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Coalescent Process ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

By applying a perturbation method to the structured coalescent process in population genetics theory, we obtain the approximate solutions of the moment generating functions for the total coalescence time, the number of segregating sites among sampled DNA sequences and the number of allele types in a sample in the case of strong migration.

A perturbation method for the structured coalescent with strong migration

2000 ◽  
Vol 37 (01) ◽  
pp. 148-167 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Population Genetics ◽  
Perturbation Method ◽  
Dna Sequences ◽  
Generating Functions ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Coalescent Process ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

By applying a perturbation method to the structured coalescent process in population genetics theory, we obtain the approximate solutions of the moment generating functions for the total coalescence time, the number of segregating sites among sampled DNA sequences and the number of allele types in a sample in the case of strong migration.

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].

scholarly journals Recurrence Relations for Marginal and Joint Moment Generating Functions of Topp-Leone Generated Exponential Distribution based on Record Values and its Characterization

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Zaki Anwar ◽  
Neetu Gupta ◽  
Mohd. Akram Raza Khan ◽  
Qazi Azhad Jamal
Keyword(s):  
Exponential Distribution ◽  
Recurrence Relation ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Moment Generating Function ◽  
Record Values ◽  
Joint Moment ◽  
Moment Generating Functions ◽  
Lower Record ◽  
Lower Record Values

The exact expressions and some recurrence relations are derived for marginal and joint moment generating functions of kth lower record values from Topp-Leone Generated (TLG) Exponential distribution. This distribution is characterized by using the recurrence relation of the marginal moment generating function of kth lower record values.

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