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R: Expectation-Maximisation for a mixture of exponential...

EM.mixexp

R Documentation

Expectation-Maximisation for a mixture of exponential distributions

Description

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

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).

Author(s)

Yves Deville

Examples

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

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/EM.mixexp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: EM.mixexp
> ### Title: Expectation-Maximisation for a mixture of exponential
> ###   distributions
> ### Aliases: EM.mixexp
> 
> ### ** 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")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>