Introduction | Review of core mathematical concepts | General Definitions | Properties and classification of states | A short example | The structure of the package | Creating markovchain objects | Handling markovchain objects | Probability with markovchain objects | Conditional distributions | Stationary states | Entropy rate | Topological entropy and normalized entropy rate | Classification of states | First passage time distributions and means | Kemeny's constant | Sensitivity of the stationary distribution | Spectral diagnostics: SLEM, spectral gap and implied timescales | Reversibility | Closest reversible approximation | Mixing time | Lazy chains | Evolution of a distribution | Mean recurrence time | Absorption probabilities and mean absorption time | Fundamental matrix | Restricting a chain to a subset of states | Committor probability | Hitting probabilities | Stochastic monotonicity | Classical Markov chain constructors | Birth-death chains | The Ehrenfest urn model | Combining two chains | The n-step chain | Population genetics: the Moran and Wright-Fisher models | Random and special chains | Statistical analysis | Simulation | Lumpability and aggregation of states | Spectral Kullback-Leibler aggregation | Serialization and export | Estimation | Prediction | Predicting from a markovchain object | Predicting from a markovchainList object | Statistical tests | Assessing the independence of consecutive states | Assessing the Markov property of a Markov chain sequence | Assessing the order of a Markov chain sequence | Assessing the stationarity and time-homogeneity of a Markov chain sequence | Divergence tests for empirically estimated transition matrices | Pseudo-Bayesian estimation | Bayesian estimation | Notation and set-up | Methods | Predictive distribution | Choosing the hyper-parameters | Usage and examples | Continuous time Markov chains | Definition and generator matrix | Stationary distributions | Estimation of the generator matrix | Expected hitting time | Transition probabilities over time | Examples | Applications | Weather forecasting | Land of Oz | Alofi Island Rainfall | Finance and Economics | Finance | Economics | Discretizing autoregressive processes | Actuarial science | MTPL Bonus Malus | Health insurance example | Sociology | Genetics and Medicine | Genetics | Medicine | Discussion, issues and future plans | Acknowledgments | References

Expected hitting time of a CTMC | Probability at time t of a CTMC | Plotting the generator matrix of a CTMC | Imprecise continuous time Markov chains | Types of ICTMCs | Lower Transition Rate Operators for ICTMCs | Lower Transition Operators | The impreciseProbabilityatT function | Generator of a CTMC from a frequency matrix | Committor of a Markov chain | First passage probability for a set of states | Mean occupation of the states during the first N steps | Expected rewards of a Markov chain | Expected rewards before hitting a set of states | Irreducibility of a CTMC | Simulation of higher order multivariate Markov chains | Time reversibility of a CTMC | References

Higher order Markov chains as mixtures of lags | Comparing models of different orders | Selecting the order of a full Markov chain | Reproducing a published comparison | The mixture transition distribution model | Prediction and simulation | Higher order multivariate Markov chains | Introduction | Representation of parameters in the code | Definition of HOMMC class | How to create an object of class HOMMC | Fit HOMMC | A marketing example | Acknowledgments | References

Introduction and general notation | Loss Distribution | Expected Loss | Limited Expected Loss | Loss Cost of a Layer | Increased Limit Factor | Exposure curves | Normalising loss experience using TIV and MPL | Analysing deductibles | Destruction rate models | Classic distributions | Uniform distribution | Beta distribution | One-inflated distributions | Characterizations | The one-inflated beta distribution | The MBBEFD distribution, first parametrization | Characterization by the exposure curve | Distribution, density and quantile functions | Moments | The MBBEFD distribution, second parametrization | Parameter domain | Fitting methods and pricing examples | Fitting methods: MLE and TLMME | Examples | Computation of premium rate (example) | Losses below deductible | Losses above deductible, but below limit | Losses above limit | Premium Rate | References