meanRecurrenceTimes: Method to get the mean recurrence times mu
In smmR: Simulation, Estimation and Reliability of Semi-Markov Models

Description Usage Arguments Details Value

Method to get the mean recurrence times μ.

1	meanRecurrenceTimes(x, klim = 10000)

`x`	An object of S3 class `smmfit` or `smm`.
`klim`	Optional. The time horizon used to approximate the series in the computation of the mean sojourn times vector m (cf. meanSojournTimes function).

Consider a system (or a component) S_{ystem} whose possible states during its evolution in time are E = \{1,…,s\}.

We are interested in investigating the mean recurrence times of a discrete-time semi-Markov system S_{ystem}. Consequently, we suppose that the evolution in time of the system is governed by an E-state space semi-Markov chain (Z_k)_{k \in N}. The state of the system is given at each instant k \in N by Z_k: the event \{Z_k = i\}.

Let T = (T_{n})_{n \in N} denote the successive time points when state changes in (Z_{n})_{n \in N} occur and let also J = (J_{n})_{n \in N} denote the successively visited states at these time points.

The mean recurrence of an arbitrary state j \in E is given by:

μ_{jj} = \frac{∑_{i \in E} ν(i) m_{i}}{ν(j)}

where (ν(1),…,ν(s)) is the stationary distribution of the embedded Markov chain (J_{n})_{n \in N} and m_{i} is the mean sojourn time in state i \in E (see meanSojournTimes function for the computation).

A vector giving the mean recurrence time (μ_{i})_{i \in [1,…,s]}.

smmR documentation built on Aug. 3, 2021, 5:07 p.m.