BlockCountProcess: Block counting process

In aumath-advancedr2019/PhaseTypeGenetics: The Phase-Type Distribution with Applications in Population Genetics

Description

Computing the state space and the corresponding rate matrix for the block counting process for a given sample size n in the standard coalescent model.

Usage

BlockCountProcess(n)

Arguments

n	the sample size (>=1)

Details

For a given sample size n, one can have one or more possible coalescent trees. Each coalescent event in these trees correspond to a state of the block counting process. Furthermore, each state is represented by a (n-1)- dimensional row vector, where each entry i corresponds to the number of branches giving rise to i descendants. Hence, state 1 is always a vector of the form (n,0,0,...,0), and state 2 is always given by the vector (n-2,1,0,...,0) eqn(n >= 3).

Value

The function returns a list containing the sub-intensity rate matrix Rate_Mat and the state space matrix StateSpace_Mat. In the latter, each row corresponds to a state and each state is a (n-1)-dimensional row vector.

Examples

a <- BlockCountProcess(4)
a$Rate_Mat
a$StateSpace_Mat

aumath-advancedr2019/PhaseTypeGenetics documentation built on Dec. 3, 2019, 7:16 a.m.