emnormmix {mritc}

Estimate the Parameters of a Normal Mixture Model Using the EM Algorithm

Description

Use the EM Algorithm to estimate the parameters of a normal mixture model.

Usage

   emnormmix(y, prop, mu, sigma, err, maxit, verbose)

Arguments

y

vector of observations.

prop

vector of initial estimate of the proportions of different components of a normal mixture model.

mu

vector of initial estimate of the means of different components of a normal mixture model.

sigma

vector of initial estimate of the standard deviations of different components of a normal mixture model.

err

relative maximum error(s) used to decide when to stop the iteration. It could be a vector of length three corresponding to the relative maximum errors of the means, standard deviations, and proportions of all components of a normal mixture model. When it is a scalar, all have the same relative maximum error.

maxit

maximum number of iterations to perform.

verbose

logical. If TRUE, then indicate the level of output as the algorithm runs after every 10 iterations.

Details

It is tailor-made for the case when observations are from a finite set (MRI data for example). The table lookup method is used to speed up the computation.

Value

prop

a vector of estimated proportions of different components of a normal mixture model.

mu

a vector of estimated means of different components of a normal mixture model.

sigma

a vector of estimated standard deviations of different components of a normal mixture model.

Examples

  prop <- c(0.3, 0.3, 0.4)
  mu <- c(-10, 0, 10)
  sigma <- rep(1, 3)
  y<- floor(rnormmix(n=100000, prop, mu, sigma)[,1])
  initial <- initOtsu(y, 2)
  emnormmix(y=y, prop=initial$prop, mu=initial$mu, sigma=initial$sigma,
            err=1e-7, maxit=100, verbose=TRUE)