hmm0norm: Parameter Estimation of an HMM with Extra Zeros
In HMMextra0s: Hidden Markov Models with Extra Zeros

Description Usage Arguments Value Author(s) References Examples

Calculates the parameter estimates of a 1-D HMM with observations having extra zeros.

1	hmm0norm(R, Z, pie, gamma, mu, sig, delta, tol=1e-6, print.level=1, fortran = TRUE)

`R`	is the observed data. `R` is a T 1* matrix, where T is the number of observations.
`Z`	is the binary data with the value 1 indicating that an event was observed and 0 otherwise. `Z` is a vector of length T.
`pie`	is a vector of length m, the jth element of which is the probability of Z=1 when the process is in state j.
`gamma`	is the transition probability matrix (m m*) of the hidden Markov chain.
`mu`	is a 1 m* matrix, the jth element of which is the mean of the (Gaussian) distribution of the observations in state j.
`sig`	is a 1 m* matrix, the jth element of which is the standard deviation of the (Gaussian) distribution of the observations in state j.
`delta`	is a vector of length m, the initial distribution vector of the Markov chain.
`tol`	is the tolerance for testing convergence of the iterative estimation process. The default tolerance is 1e-6. For initial test of model fit to your data, a larger tolerance (e.g., 1e-3) should be used to save time.
`print.level`	controls the amount of output being printed. Default is 1. If `print.level=1`, only the log likelihoods and the differences between the log likelihoods at each step of the iterative estimation process, and the final estimates are printed. If `print.level=2`, the log likelihoods, the differences between the log likelihoods, and the estimates at each step of the iterative estimation process are printed.
`fortran`	is logical, and determines whether Fortran code is used; default is `TRUE`.

`pie`	is the estimated probability of Z=1 when the process is in each state.
`mu`	is the estimated mean of the (Gaussian) distribution of the observations in each state.
`sig`	is the estimated standard deviation of the (Gaussian) distribution of the observations in each state.
`gamma`	is the estimated transition probability matrix of the hidden Markov chain.
`delta`	is the estimated initial distribution vector of the Markov chain.
`LL`	is the log likelihood.

Ting Wang

Wang, T., Zhuang, J., Obara, K. and Tsuruoka, H. (2016) Hidden Markov Modeling of Sparse Time Series from Non-volcanic Tremor Observations. Journal of the Royal Statistical Society, Series C, Applied Statistics, 66, Part 4, 691-715.

pie <- c(0.002,0.2,0.4)
gamma <- matrix(c(0.99,0.007,0.003,
                  0.02,0.97,0.01,
                  0.04,0.01,0.95),byrow=TRUE, nrow=3)
mu <- matrix(c(0.3,0.7,0.2),nrow=1)
sig <- matrix(c(0.2,0.1,0.1),nrow=1)
delta <- c(1,0,0)
y <- sim.hmm0norm(mu,sig,pie,gamma,delta, nsim=5000)
R <- as.matrix(y$x,ncol=1)
Z <- y$z
yn <- hmm0norm(R, Z, pie, gamma, mu, sig, delta)
yn