| PCMPExpxMeanExp {PCMBase} | R Documentation |
Create a function of time that calculates (1-exp(-lambda_ij*time))/lambda_ij
for every element lambda_ij of the input matrix Lambda_ij.
Description
Create a function of time that calculates (1-exp(-lambda_ij*time))/lambda_ij
for every element lambda_ij of the input matrix Lambda_ij.
Usage
PCMPExpxMeanExp(
Lambda_ij,
threshold.Lambda_ij = getOption("PCMBase.Threshold.Lambda_ij", 1e-08)
)
Arguments
Lambda_ij |
a squared numerical matrix of dimension k x k |
threshold.Lambda_ij |
a 0-threshold for abs(Lambda_i + Lambda_j), where Lambda_i and Lambda_j are eigenvalues of the parameter matrix H. This threshold-value is used as a condition to take the limit time of the expression '(1-exp(-Lambda_ij*time))/Lambda_ij' as '(Lambda_i+Lambda_j) –> 0'. You can control this value by the global option "PCMBase.Threshold.Lambda_ij". The default value (1e-8) is suitable for branch lengths bigger than 1e-6. For smaller branch lengths, you may want to increase the threshold value using, e.g. 'options(PCMBase.Threshold.Lambda_ij=1e-6)'. |
Details
the function (1-exp(-lambda_ij*time))/lambda_ij corresponds to the product
of the CDF of an exponential distribution with rate Lambda_ij multiplied by its mean value (mean waiting time).
Value
a function of time returning a matrix with entries formed from the
above function or the limit, time, if |Lambda_{ij}|<=trehshold0.