mixtools (version 0.1.0)

normalmixEM: EM Algorithm for Mixtures of Univariate Normals

Description

Return EM algorithm output for mixtures of normal distributions.

Usage

normalmixEM(x, lambda = NULL, mu = NULL, sigma = NULL, k = 2,
            arbmean = TRUE, arbvar = TRUE, epsilon = 1e-08, 
            maxit = 10000, verb = FALSE)

Arguments

x

A vector of length n consisting of the data.

lambda

Initial value of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by mu.

mu

A k-vector of initial values for the mean parameters. If NULL, then the vector is generated from a normal distribution according to a binning method done on the data. If both lambda and mu are NULL, then number of com

sigma

A k-vector of initial values for the standard deviation parameters. If NULL, then 1/sigma$^2$ has random exponential entries according to a binning method done on the data. If lambda, mu, and sigm

k

Number of components. Ignored unless lambda, mu, and sigma are all NULL.

arbmean

If TRUE, then the component densities are allowed to have different mus. If FALSE, then a scale mixture will be fit.

arbvar

If TRUE, then the component densities are allowed to have different sigmas. If FALSE, then a location mixture will be fit.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

• normalmixEM returns a list of class mixEM with items:
• x
  The raw data.
• lambda
  The final mixing proportions.
• mu
  The final mean parameters.
• sigma
  The final standard deviations. If arbmean = FALSE, then only the smallest standard deviation is returned. See scale below.
• scale
  If arbmean = FALSE, then the scale factor for the component standard deviations is returned. Otherwise, this is omitted from the output.
• loglik
  The final log-likelihood.
• posterior
  An nxk matrix of posterior probabilities for observations.
• all.loglik
  A vector of each iteration's log-likelihood.
• ft
  A character vector giving the name of the function.

References

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley & Sons, Inc.

See Also

mvnormalmixEM

Examples

##Analyzing the Old Faithful geyser data with a 2-component mixture of normals.

data(faithful)
attach(faithful)
out<-normalmixEM(waiting, arbvar = FALSE)
out