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

## Description

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

## Usage

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

## Arguments

 `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`.

## Value

 `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

## References

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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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 ```

HMMextra0s documentation built on Aug. 3, 2021, 9:06 a.m.