Expectation-Maximisation for a mixture of exponential distributions

Experimental function for Expectation-Maximisation (EM) estimation

Usage

EM.mixexp(x, m = 2)

Arguments

x

Sample vector with values >0.

m

Number of mixture components.

Details

The EM algorithm is very simple for exponential mixtures (as well as for many other mixture models).

According to a general feature of EM, this iterative method leads to successive estimates with increasing likelihood but which may converge to a local maximum of the likelihood.

Value

List with

estimate

Estimated values as a named vector.

logL

Vector giving the log-likelihood for successive iterations.

Alpha

Matrix with m columns giving probability weights for successive iterations. Row with number it contains the m probabilities at iteration it.

Theta

Matrix with m columns giving the estimates of the m expectations for the successive iterations

Author

Yves Deville

Note

The estimation is done for expectation (inverse rates) but the estimate vector in the result contains rates for compatibility reasons (e.g with exponential).

Examples

set.seed(1234)
x <- rmixexp2(n = 100, prob1 = 0.5, rate2 = 4)
EM.mixexp(x) -> res
res$estimate
#>     prob1     prob2     rate1     rate2 
#> 0.5844083 0.4155917 1.2991665 4.7291873 
matplot(res$Theta, type = "l", lwd = 2,
        xlab = "iteration", ylab = "theta",
        main = "exponential inverse rates")