# distributionSet: Set the parameters for the distributions of observations In RHmm: Hidden Markov Models Simulations and Estimations

## Description

This function is used to create a distributionClass object which contains the parameters of the distribution of the observations for each hidden state. Since distributions can be univariate or multivariate, discrete or continuous, the different values of a distributionClass object depend of the nature of the distribution.

## Usage

 `1` ```distributionSet(dis, ...) ```

## Arguments

 `dis` Name of the distribution of observations. In 'NORMAL', 'DISCRETE', 'MIXTURE'. `...` Other parameters. See details.

## Details

Typical usages are:

• distributionSet(dis="NORMAL", mean, var)

• distributionSet(dis="NORMAL", mean, cov)

• distributionSet(dis="MIXTURE", mean, var, proportion)

• distributionSet(dis="MIXTURE", mean, cov, proportion)

• distributionSet(dis="DISCRETE", proba, labels=NULL)

The parameters are:

mean

- Univariate normal distribution: a vector of the means for each state of the model.
- Multivariate normal distribution: a list of the mean vectors for each state of the model.
- Mixture of univariate normal distribution: a list of vectors of the mixture means for each state of the model.
- Mixture of multivariate normal distribution: a list of lists of vectors of means for each state and each component of the mixture of the model.

var

- Univariate normal distribution: a vector of the variances for each states of the model.
- Mixture of univariate normal distribution: a list of vectors of the mixture variances for each states of the model.

cov

- Multivariate normal distribution: a list of covariance matrices of the multivariate normal distribution for each state of the model
- Mixture of multivariate normal distribution: a list of list of covariance matrices for each state and each component of the mixture.

proportion

A list of vector of the mixture proportions for each state of the model.

proba

A list of vector of discrete probabilities for each state of the model.

labels

A vector of the labels of the discrete observations. Default NULL.

## Value

An ‘distributionClass’ class object with some of the following elements:

dis

The name of the distribution.

nStates

Number of hidden states.

dimObs

Dimension of observations.

nMixt

Number of mixtures for mixture of normal distributions.

nLevels

Number of levels for discrete distributions.

mean

The ‘mean’ argument for univariate normal, mixture of univariate normal and multivariate normal distributions.

var

The ‘var’ argument for univariate normal and mixture of univariate normal distributions

cov

The ‘cov’ argument for multivariate normal and mixture of multivaiate normal distributions

proba

The ‘proba’ argument for discrete distributions

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51``` ``` # 3 hidden states Markov Model with univariate normal distributions # for the observations # obs | hidden state = 1 are N(1, 1) # obs | hidden state = 2 are N(-2, 2) # obs | hidden state = 3 are N(5, 4) n_1d_3s <- distributionSet("NORMAL", mean=c(1, -2, 5), var=c(1, 2, 4)) # 2 hidden states Markov Model with bivariate normal distributions # for the observations # obs | hidden state = 1 are N(m1, cov1) # obs | hidden state = 2 are N(m2, cov2) m1 <- c(1,1) m2 <- c(-2, -2) cov1 <- matrix(c(1, 1, 1, 4), nrow=2) cov2 <- matrix(c(1, -1, -1, 9), nrow=2) n_2d_2s <- distributionSet("NORMAL", mean=list(m1, m2), cov=list(cov1, cov2)) # 3 hidden states Markov Model with a mixture of two normal # distributions for the observations # obs | hidden state = i are: # pi[1] * N(mmi[1], vari[1]) + pi[2] * N(mmi[2], vari[2]) mm1 <- c(1, -1) mm2 <- c(-2, 2) mm3 <- c(5, 5) var1 <- c(1, 2) var2 <- c(2, 3) var3 <- c(1, 1) p1 <- c(0.5, 0.5) p2 <- c(0.8, 0.2) p3 <- c(0.3, 0.7) mn_2s <- distributionSet("MIXTURE", mean=list(mm1, mm2, mm3), var=list(var1, var2, var3), proportion=list(p1, p2, p3)) # 2 hidden states Markov Model with discrete observations dp1 <- c(0.2, 0.3, 0.3, 0.2) dp2 <- c(0.1, 0.1, 0.1, 0.7) labels <- c("I", "M", "A", "G") d_2s <- distributionSet("DISCRETE", proba=list(dp1, dp2), labels=labels) # 2 hidden states Markov model with mixture of 3 2-d gaussian distribution q1 <- rep(1/3, 3) q2 <- runif(3) q2 <- q2/sum(q2) cov3 <- matrix(c(1,2,2,10), nrow=2) cov4 <- matrix(c(1, 0, 0, 1), nrow=2) cov5 <- matrix(c(2,4,4,50), nrow=2) cov6 <- matrix(c(25,1, 1, 2), nrow=2) mm4 <- c(100, 20) mm5 <- c(20, -20) mm6 <- c(0, 0) m_2d_2s <- distributionSet("MIXTURE", mean=list(list(mm1,mm2,mm3), list(mm4,mm5,mm6)), cov=list(list(cov1,cov2,cov3), list(cov4,cov5,cov6)), proportion=list(q1,q2)) ```

RHmm documentation built on May 2, 2019, 6:53 p.m.