linksrm_convert {PtProcess}

Parameter Conversion for Linked Stress Release Model

Description

Converts parameter values between two different parameterisations (described in Details below) of the linked stress release model.

Usage

linksrm_convert(params, abc=TRUE)

Arguments

params

a vector of parameter values of length n^2+2n, where n is the number of regions in the model.

abc

logical. If TRUE (default), then the input value of params is that of the abc parameterisation. See Details for further explanation.

Details

If abc == TRUE, the conditional intensity for the ith region is assumed to have the form

\lambda_g(t,i | {\cal H}_t) = \exp\left\{ a_i + b_i\left[t - \sum_{j=1}^n c_{ij} S_j(t)\right]\right\}

with params = (a_1, \cdots, a_n, b_1, \cdots, b_n, c_{11}, c_{12}, c_{13}, \cdots, c_{nn}).

If abc == FALSE, the conditional intensity for the ith region is assumed to have the form

\lambda_g(t,i | {\cal H}_t) = \exp\left\{ \alpha_i + \nu_i\left[\rho_i t - \sum_{j=1}^n \theta_{ij} S_j(t)\right]\right\}

where \theta_{ii}=1 for all i, n = \sqrt{\code{length(params)} + 1} - 1, and params

= (\alpha_1, \cdots, \alpha_n, \nu_1, \cdots, \nu_n, \rho_1, \cdots, \rho_n, \theta_{12}, \theta_{13}, \cdots, \theta_{1n}, \theta_{21}, \theta_{23}, \cdots, \theta_{n,n-1}).

Value

A list object with the following components is returned:

params

vector as specified in the function call.

a

vector of length n as in the abc parameterisation.

b

vector of length n as in the abc parameterisation.

c

n by n matrix as in the abc parameterisation.

alpha

vector of length n as in the alternative parameterisation.

nu

vector of length n as in the alternative parameterisation.

rho

vector of length n as in the alternative parameterisation.

theta

n by n matrix with ones on the diagonal as in the alternative parameterisation.

See Also

linksrm_gif