smmR-package: smmR : Semi-Markov Models, Markov Models and Reliability

In corentin-dev/smmR: Simulation, Estimation and Reliability of Semi-Markov Models

smmR : Semi-Markov Models, Markov Models and Reliability

Description

This package 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. Estimation and simulation of discrete-time k-th order Markov chains are also considered.

Semi-Markov models are specified by using the functions smmparametric() and smmnonparametric() for parametric and non-parametric specifications respectively. These functions return objects of S3 class (smm, smmparametric) and (smm, smmnonparametric) respectively (smm class inherits from S3 classes smmparametric or smmnonparametric). Thus, smm is like a wrapper class for semi-Markov model specifications.

Based on a model specification (an object of class smm), it is possible to:

• simulate one or several sequences with the method simulate.smm();

• plot conditional sojourn time distributions (method plot.smm());

• compute log-likelihood, AIC and BIC criteria (methods logLik(), AIC(), BIC());

• compute reliability, maintainability, availability, failure rates (methods reliability(), maintainability(), availability(), failureRate()).

Estimations of parametric and non-parametric semi-Markov models can be done by using the function fitsmm(). This function returns an object of S3 class smmfit. The class smmfit inherits from classes (smm, smmparametric) or (smm, smmnonparametric).

Based on a fitted/estimated semi-Markov model (an object of class smmfit), it is possible to:

• simulate one or several sequences with the method simulate.smmfit();

• plot estimated conditional sojourn time distributions (method plot.smmfit());

• compute log-likelihood, AIC and BIC criteria (methods logLik(), AIC(), BIC());

• compute estimated reliability, maintainability, availability, failure rates and their confidence intervals (methods reliability(), maintainability(), availability(), failureRate()).

Author(s)

Maintainer: Nicolas Vergne [e-mail]

Authors:

• Vlad Stefan Barbu (ORCID)

• Florian Lecocq

• Corentin Lothode (ORCID)

Other contributors:

• Caroline Berard [contributor]

• Dominique Cellier [contributor]

• Mathilde Sautreuil [contributor]

References

V. S. Barbu, N. Limnios. (2008). Semi-Markov Chains and Hidden Semi-Markov Models Toward Applications - Their Use in Reliability and DNA Analysis. New York: Lecture Notes in Statistics, vol. 191, Springer.

R.E. Barlow, A.W. Marshall, and F. Prochan. (1963). Properties of probability distributions with monotone hazard rate. Ann. Math. Statist., 34, 375-389.

T. Nakagawa and S. Osaki. (1975). The discrete Weibull distribution. IEEE Trans. Reliabil., R-24, 300-301.

D. Roy and R. Gupta. (1992). Classification of discrete lives. Microelectron. Reliabil., 32 (10), 1459-1473.

I. Votsi & A. Brouste (2019) Confidence interval for the mean time to failure in semi-Markov models: an application to wind energy production, Journal of Applied Statistics, 46:10, 1756-1773.

See Also

Useful links:

• https://plmlab.math.cnrs.fr/lmrs/statistique/smmR

• https://lmrs.pages.math.cnrs.fr/statistique/smmR

• Report bugs at https://github.com/corentin-dev/smmR/issues

corentin-dev/smmR documentation built on April 14, 2023, 11:36 p.m.