getKernel

Computes the semi-Markov kernel \(q_{ij}(k)\).

Performs parametric and non-parametric estimation and simulation
for multi-state discrete-time semi-Markov processes. For the parametric
estimation, several discrete distributions are considered for the sojourn
times: Uniform, Geometric, Poisson, Discrete Weibull and Negative Binomial.
The non-parametric estimation concerns the sojourn time distributions,
where no assumptions are done on the shape of distributions. Moreover, the
estimation can be done on the basis of one or several sample paths, with or
without censoring at the beginning or/and at the end of the sample paths.
Reliability indicators such as reliability, maintainability, availability,
BMP-failure rate, RG-failure rate, mean time to failure and mean time to
repair are available as well. The implemented methods are described in
Barbu, V.S., Limnios, N. (2008) <doi:10.1007/978-0-387-73173-5>,
Barbu, V.S., Limnios, N. (2008) <doi:10.1080/10485250701261913> and
Trevezas, S., Limnios, N. (2011) <doi:10.1080/10485252.2011.555543>.
Estimation and simulation of discrete-time k-th order Markov chains are
also considered.

Nicolas Vergne

smmR

Simulation, Estimation and Reliability of Semi-Markov Models

Vlad Stefan Barbu

Florian Lecocq

Corentin Lothode

getKernel function

<dl><dt>x</dt>
<dd>An object of S3 class <code>smmfit</code> or <code>smm</code>.</dd>
<dt>k</dt>
<dd>A positive integer giving the time horizon.</dd>
<dt>var</dt>
<dd>Logical. If <code>TRUE</code> the asymptotic variance is computed.</dd>
<dt>klim</dt>
<dd>Optional. The time horizon used to approximate the series in the
computation of the mean sojourn times vector \(m\) (cf.
meanSojournTimes function) for the asymptotic variance.</dd></dl>

Arguments

Method to get the semi-Markov kernel \(q\) — getKernel

<dl>

<dt>x</dt>
<dd>An object of S3 class <code>smmfit</code> or <code>smm</code>.</dd>


<dt>k</dt>
<dd>A positive integer giving the time horizon.</dd>


<dt>var</dt>
<dd>Logical. If <code>TRUE</code> the asymptotic variance is computed.</dd>


<dt>klim</dt>
<dd>Optional. The time horizon used to approximate the series in the
computation of the mean sojourn times vector \(m\) (cf.
meanSojournTimes function) for the asymptotic variance.</dd>

</dl>

getKernel: Method to get the semi-Markov kernel \(q\)

Description

Usage

Value

Arguments